Canterbury Puzzles

I JULIUS WANOENMEIM

i

I

THE CANTERBURY PUZZLES

THE CANTERBURY PUZZLES OTHER CURIOUS PROBLEMS

BY

HENRY ERNEST DUDENEY

ILLUSTRATED BT PAUL HARDY, THE AUTHOR AND OTHERS

E.

P.

NEW YORK BUTTON AND COMPANY 1908

f

Printed in England.

IN expressing his acknowledgments to the periodical Press, the author of

this

book desires

in particular to

thank the proprietors

The London Magazine, The Strand Magazine, The Royal Magazine, C. B. Fry s Magazine, The Captain, The World and of

His Wife, The Penny Pictorial Magazine, Tit-Bits, The Daily Mail, The Tribune, and The Weekly Dispatch, for their courtesy in allowing

appeared

him

in their pages.

able quantity of is

better."

and problems of his that have Though the volume contains a consider

to reprint articles

new

" matter,

it

sometimes happens that

the old

CONTENTS INTRODUCTION

....

PAGE xi

THE CANTERBURY PUZZLES

1

PUZZLING TIMES AT SOLVAMHALL CASTLE

THE MERRY MONKS OF RIDDLEWELL THE STRANGE ESCAPE OF THE KING S

THE ADVENTURES OF THE PUZZLE CLUB

.

... ... ...

JESTER

THE SQUIRE S CHRISTMAS PUZZLE PARTY

.

.

.

33

42 51

58

66

THE PROFESSOR S PUZZLES

81

MISCELLANEOUS PUZZLES

89

SOLUTIONS

131

INTRODUCTION READERS

"The

of

Mill

on the Floss"

will

remember

whenever Mr. Tulliver found himself confronted by any " difficulty he was accustomed to make the trite remark,

There can be no denying the

puzzling world."

fact that

surrounded on every hand by posers, some of which the

man

has mastered, and

Solomon

of solution.

men

sharp as most

many

of

himself,

which may be

who may be

at solving

not

:

the

upon a rock

way

of a

;

man

way way

of

the

an eagle

only lives

in

discover diseases,

we

a

are

intellect of

be impossible

supposed to have been as

me

in the air

;

;

which

yea, four

the

of a ship in the midst of

way

I

of a serpent

the sea

;

and the

with a maid."

Probing into the secrets

we

It s

a puzzle, had to admit "there be

three things which are too wonderful for

know

said to

that little

of

Nature

is

select different lines of research.

a passion with

Men

all

men

;

have spent long

such attempts as to turn the baser metals into gold, to perpetual

and

motion,

to

find

a cure for certain

malignant

to navigate the air.

From morning

to night

we

are being perpetually brought face to

But there are puzzles and puzzles. Those that are usually devised for recreation and pastime may be roughly divided into two classes Puzzles that are built up on some face with puzzles.

:

-

-=*

"

xi

INTRODUCTION interesting or informing

little

principle

and puzzles

;

no

that conceal

such as a picture cut at random into

principle whatever

little bits

to

be put together again, or the juvenile imbecility known as the "

" rebus," or

to

latter

to the

amusement

former species

of the

man

sane

may be

or

woman

said

the

;

can be confidently recommended to the feeble-minded.

The

curious propensity for propounding puzzles

any race or

to

of history.

any period

It is

is

always showing

be a Sphinx a Chinese

of

itself

in different

mathematician makes

of

lore,

an Indian or

Tibet,

a

fakir,

European

and

are

artisan

engaged

perpetually

attempting to solve puzzles, while every game, sport, and pastime built

up

of

The

of greater or less difficulty.

problems

it

difference.

little

scientist,

mahatma

a

;

though

lived,

whether the individual

Hebrew

Egypt, a Samson of

philosopher,

Theologian,

forms

not peculiar to

simply innate in every

man, woman, and child that has ever

intelligent is

The

picture puzzle."

be adapted

in is

spontaneous

question asked by the child of his parent, by one cyclist of another

while taking a brief

rest

on a

by a cricketer during the

stile,

luncheon hour, or by a yachtsman

lazily

frequently a problem of considerable

scanning the horizon,

difficulty.

propounding puzzles to one another every day always knowing

A good

we

In short of our lives

are

is

all

without

it.

puzzle should

demand

the exercise of our best wit and

mathematics and a certain

ingenuity,

and although a knowledge

familiarity

with the methods of logic are often of great service in the

solution of

these things, yet

natural cunning

and

sagacity

it

is

of

sometimes happens that a kind of considerable value.

For many

of

of

the best problems cannot be solved by any familiar scholastic methods,

but must be attacked on entirely original

and wide experience, one

lines.

This

is

why,

finds that particular puzzles will

after a long

sometimes

be solved more readily by persons possessing only naturally faculties

than by the better educated. xii

The

alert

best players of such

INTRODUCTION puzzle games as chess and draughts are not mathematicians, though just possible that often

it is

may have undeveloped mathematical

they

minds. It is

many

we

extraordinary what fascination a good puzzle has for a great

We

people.

know

are impelled to master

a pleasure and a sense

reward

What

is

like to

enigma

and

be puzzled

The

?

But

enough. is

why

simply that

that the pleasure

was

A good puzzle,

many

all

has solved

The

in later life artists

heroes,

We have

it

is

and he

spirit of rivalry is

men

turns

and

(if

ever attempt to do

done

it

it,

?

the seeking and finding for their

in

like virtue,

its is

own reward.

Man

own loves

not entirely happy until he

our mental inferiority to those

innate in

smallest child, in play or education, to

and

Why

that directly the

is

gave us pleasure to seek the solution

it

We never like to feel

it.

us.

we

is

be won.

to

find irresistible*

curious thing

did

be confronted by a mystery

around

no prize

is

solved the interest generally vanishes.

is

The answer sakes.

that

importance, yet

succeeded there

are a quite sufficient

that

satisfaction

mysterious charm

this

is

that

of

trivial

we have

and when

it,

even when there

for our trouble,

do we

to

the thing to be of

man

keep

it

;

level

stimulates the

with his fellows,

into great discoverers, inventors, orators,

they have

more

material

aims)

perhaps

millionaires.

In starting on a tour through the

well to

remember

that

varied character. often

make

I

we

shall

shall take

wide realm

of

meet with points advantage of

this variety.

the mistake of confining themselves to one

the realm, and thereby missing opportunities of lie

within their

acrostics

reach around

them.

One

and other word puzzles, another

rackers, another to chess problems

the chess-board, and have chess),

Puzzledom we do

of interest of a

and so

on.

This

little is

new

little

corner of

pleasures that

person will keep to

to mathematical brain-

(which are merely puzzles on

practical relation to the

a mistake, because xiii

very

People so

it

game

restricts

of

one

s

INTRODUCTION and neglects

pleasures,

that

which

variety

so

is

the

for

good

brain.

And

there

exercise

really a practical utility in puzzle-solving.

is

body, and in both cases of

by the doctor the

brain,

but

it

in

from

as the doing

walk recommended

daily

daily exercise for

appear to be so much waste

economy

the

in

"

woman who was

cob wigs on the brain."

apt

to

suffer

equal

to

the

very

nothing

sweeping them away.

from

mental of

solving

They keep

they useful in

this indirect

teaching us some the affairs of

little

us

of

there

problems

is

for

stimulate the

alert,

faculties.

many

And

not only are

way, but they often directly help us by "

and

tricks

at the

life

and

the brain

imagination and develop the reasoning

convinced

and

cobwebs,

puzzles

;

one

in

This may be a

very rare complaint, but in a more metaphorical sense, are

time

of

Albert Smith,

end.

a

describes

amusing novels,

that she suffered

The

of the body, or the

good

itself

truest

much what we do

not so

it is

derive benefit.

for the

may

the

is

his

of

we

from which

it

Regular

supposed to be as necessary for the brain as for the

is

"

be applied

that can

wrinkles

most unexpected times, and

in

in

the most

unexpected ways.

There

is

an interesting passage

letters of Fitzosborne.

of

making and

Here

is

in praise of puzzles in the quaint

solving puzzles

both sexes.

encouragement

It

knows not you

of

method

shortest logic.

It is

art,

how

knows not how

The

ingenious study

most

I

part in the meditation

would recommend it

to the

affords the easiest

and

conveying some of the most useful principles of of

to dissemble it

make a

indeed, that

both the Universities, as

of

was the maxim

to receive

How

an

:

a science undoubtedly of

is

necessary acquirement, and deserves to of

"

an extract

a

as mine, that "

he

very wise prince that

knows not how he

to reign

who knows

not

;

and

how

I

who

desire

to riddle

to live/

are good puzzles invented

?

xiv

I

am

not referring to acrostics,

INTRODUCTION and

charades,

anagrams,

that sort

of

but to puzzles that

thing,

contain an original idea.

Well, you cannot invent a good puzzle to more than you can invent anything else in that manner. Notions for puzzles come at strange times and in strange ways.

order, any

are suggested by something

They

by other puzzles " will

I

way

of creating

You may make

It

is

you can only make use wrong, because an expert

is

of

it

to

useless to say,

when

no

is

comes.

it

in these things will

scores of puzzles while another person, equally clever, cannot

"

we

to save his life," as

The

simple.

by

notice.

up

invent an original puzzle," because there

an idea

think this

invent one

by

see or hear, and are led

come under our

that

down and

sit

we

The

say.

expert knows an idea when he

long experience to judge of

its

value.

explanation

sees one,

is

and

is

Fertility, like facility,

very able

comes

practice.

Sometimes a new and most

interesting idea

is

A

blunder of somebody over another puzzle.

suggested by the

boy was given a

puzzle to solve by a friend, but he misunderstood what he had to do,

about attempting what most likely everybody would have

and

set

told

him was

stuck at

When

his friend

intended thing

and

saw the

solution,

"

greater is

now

Puzzles can be

And

!

wire or

string, all

come

have been made out nine It

little digits

and

will,

and he

actually succeeded.

This

is

not the puzzle

I

but you have found out some

puzzle books.

out of almost anything, in the hands of the

ingenious person with an idea. of

" said,

he

the puzzle which that boy accidentally

in all the old

made

on, until

he

me

you misunderstood

much

discovered

But he was a boy with a

impossible.

for six months, off

it

Coins, matches, cards, counters, bits

in useful.

An immense number of

of the letters of the alphabet,

cipher,

1,

2, 3, 4, 5, 6, 7, 8, 9,

puzzles

and from those and

0.

should always be remembered that a very simple person

may

propound a problem that can only be solved by clever heads if

at

all.

A

" child

asked,

Can God do xv

"

everything ?

On

INTRODUCTION receiving an affirmative reply, she at once said " make a stone so heavy that can t lift it ?

He

grown-up people do not difficulty lies

which

question,

destroy His

own omnipotence "

other question,

came

in contact

Many

wide-awake

once see a satisfactory answer. "

amounts

really

to "

?

asking, It

What would happen

if

with an immovable body

a contradiction in terms, for

Can

an

to the

moving body

Here we have

?

of the

Almighty

similar

irresistible

"

Yet the

form

the

somewhat

is

He

Then can

the absurd, though cunning,

in

merely

at

" :

simply

there existed such a thing as an

if

immovable body there could not

at the

same time exist a moving body

that nothing could resist.

Professor Tyndall used to invite children to ask him puzzling

them were very hard nuts to crack. One asked him why that part of a towel that was dipped in water

questions,

child

was

and some

of

of a darker colour than the

give the correct reply

How many readers could

dry part.

Many

?

people are satisfied with the most "

Why

If you ask, ridiculous answers to puzzling questions. " " nine people out of ten will reply, see through glass ?

transparent," which

is

"

Because

we

is,

can see through

Puzzles have such an to

divide

them

into

character that the best types.

of course, simply another

we

we it

of saying,

it."

infinite variety that

distinct

way

can

Because

can do

Let us takejhi^e_jirJo

is

it is

They

classes.

to sort

L

|

-exdiiiplt y

practically impossible

often

them ill

so

into a

in

merge

few broad

illustration of

what

I

mean. ^First there

and play

of

is

the ancient Riddle, that draws upon the imagination

fancy.

Readers

will

who propounded

Sphinx, the monster of Bceotia inhabitants

and devoured them

remember the

if

riddle

of

the

enigmas to the

they failed to solve them.

It

was

Sphinx would destroy herself if one of her riddles was " What animal walks on It was this ever correctly answered.

said that the

:

"

four legs in the morning,

two

at noon,

xvi

and three

in the

evening

?

INTRODUCTION was explained by CEdipus, who pointed out that man walked on his hands and feet in the morning of life, at the noon of life he It

walked

erect,

and

with a

infirmities

the evening of his days he

in

When

stick.

supported his

the Sphinx heard this explanation,

she dashed her head against a rock and immediately expired.

shows that puzzle solvers may be

Then the

first

there

and

The

was

riddle

this

" :

Out

in the

came

forth sweetness.

of a

body

dead

"

perhaps

came forth meat, and

The answer

To-day

lion."

is

garments for a correct solution.

of the eater *

the strong

It

on record, the prize being

line

of

changes

thirty

this

in

This

on occasion.

the riddle propounded by Samson.

is

prize competition

thirty sheets

really useful

was,

"A

out of

honeycomb

this sort of riddle survives in

"

Why

does a chicken cross the road ? to which as, " To get to the other side," though most people give the answer, such a form

the correct reply into the

example,

we

"To worry

the chauffeur."

It

is

has degenerated

usually based on a mere pun. *

?

a- jar")

is

have been asked from our infancy, "

not a door it is

is,

conundrum, which

and here again the answer not the correct one.

It

When

is

usually furnished ("

When

should be,

For

a door

When it

is

a

negress (an egress)."

There little

is

the large class of Letter Puzzles, which are based on the

peculiarities of the

language in which they are written

such as

In this class we anagrams, acrostics, word-squares, and charades. read backwards that also find palindromes, or words and sentences ancient must be These and forwards alike. indeed, if it be very true that

Adam

introduced himself to

Eve "

be

it

noted) with the palindromic words,

Then we have diversity.

English language,

Madam,

I

m

Arithmetical Puzzles, an immense

These range from the puzzle

be nothing but a

(in the

Adam." class,

full

of

that the algebraist finds to

" simple equation," quite easy of direct solution,

up

to the profoundest

of

numbers.

problems

in

the elegant domain of the theory

INTRODUCTION Next we have the Geometrical Puzzle, a ancient branch of

which

is

and very

favourite

the puzzle in dissection, requiring some

plane figure to be cut into a certain number of pieces that will fit

Most

together and form another figure.

in the

and

streets

wire puzzles sold

of the

concerned with the geometry of

toy- shops are

position.

But these

when we

do not nearly embrace

classes

all

kinds of puzzles even

allow for those that belong at once to several of the classes,

There are many ingenious mechanical puzzles as they stand quite alone

classify,

chess, in draughts, in cards, trick

to

is

and

that

you cannot

there are puzzles in logic, in

;

dominoes, while every conjuring

in

nothing but a puzzle, the solution to which the performer

tries

keep to himself.

There are puzzles that look easy and are easy, puzzles that look easy and are difficult, puzzles that look difficult and are difficult, and puzzles that look difficult and are easy, and in each class we may of course have degrees of easiness and

But

difficulty.

does not

it

follow that a puzzle that has conditions that are easily understood

by the merest child

is

Such a puzzle might, however,

in itself easy.

look simple to the uninformed, and only prove to be a very hard nut to

him

after

he had

actually tackled

it.

For example, if we write down nineteen ones to form the number 1,111,111,111,111,111,111, and then ask for a number (other

than

Nobody or not.

1

are

conditions

in the If

or

itself)

that will divide

but

perfectly simple,

the

it

without remainder, the task

is

terribly difficult.

world knows yet whether that number has a divisor

you can

find one,

you

will

have succeeded

in

doing

something that nobody else has ever done.

The number composed

seventeen ones, 11,111,111,111,111,

of

111, has only these two divisors, 2,071,723 and 5,363,222,357,

and

their

discovery

is

number composed only

an exceedingly heavy of

ones

that

xviii

we know

task.

The

only

with certainty to

INTRODUCTION have no divisor

is

1

Such a number

I .

is,

of course, called a

prime

number.

The maxim

that there

doing anything

Here

puzzles.

a wrong

way

of

a very marked degree to the solving of

wrong way

the

without metho37 hoping to

way and

always a right

is

applies in

making aimless

in

consists

trials

on the lmswer""fay accident,r-

hit

that generally results in our getting hopelessly entangled in the trap

that has

been

artfully laid for us.

Occasionally, however, a problem

though

it

may be

trial,

do by a process of pure reason. But method is the only one that gives any real

When we

sit

make

sure,

For

we do

if

down

to solve a puzzle,

it

very

is

not

it.

We "

first

all

If a man who was asked the question, will a dozen how much three-halfpence,

several unsuccessful attempts

he gave

it

to

latter

pleasure.

the

do

thing to

know

is

to

the conditions.

that

very likely to succeed in doing

that,

difficult

most cases the

in

we understand can, understand what it is we have to

so far as

we

such a character

of

is

solved immediately by

do,

we

are not

the story of the

herring and a half cost "

After

herrings cost ?

up,

when

the propounder

explained to him that a dozen herrings would cost a shilling. " " " I was working exclaimed the other apologetically, Herrings !

it

out in haddocks It

" !

sometimes requires more care than the reader might suppose

so to

word

clear

and exact and not so I

thing.

the conditions of a

person

who was

destroy

all

interest

that

the

required

" fewest possible straight lines/

either very clever or very foolish (I

in

and a

have never

claimed to have solved it in only one " I have taken care to make all because, as she said,

determined which)

straight line,

"

the

puzzle that they are at once

prolix as to

remember once propounding a problem

something to be done in the

quite

new

others

quibble

crooked

!

Who

could

?

xix

have

anticipated

such

a

INTRODUCTION "

Then have

you give a

if

be got over

to

combination

or

master the

in a

of

on the use

such

all

all

Of

!

all

;

boat

and he then

falls

back

once thought

I

swim

across without using

is

it

as

the

We

perfectly legitimate.

to

resort

last

have

whether a puzzle contains a

should never hastily assume

is

had

I

this class.

;

trick

we

but

over the conditions

to

the

a particular puzzle of

the people

fails

to pull

some few puzzles are intended to be kind and if there happens to be no

our best judgment

catch or not

;

stream.

tricks in

course,

without the

use

to

forbidden

is

solved by some trick of this solution

would-be solver

directly the

of a current in the

But a sapient reader made the boat at

puzzle, in

he boldly introduces a rope

say that a rope

carefully excluded

which people only hold a certain number

boat that will

persons,

difficulty

You

across.

"

crossing the river

of

To

it.

quibble

the defeated would-be

solver.

Sometimes people twists

me

the

which

will

attempt to bewilder you by curious

the meaning of words.

in

old

familiar

problem,

a monkey, but as the boy walks the monkey turns on the

is

Does the

pole so as to be always facing him on the opposite side.

boy go around the monkey

me

answer.

Of

way.

therefore,

I,

" ?

course,

As was

replied that "

way

as

said that, taking the certainly

words

the

first

give

see

all

sides

of

obvious reply that consequently a blind

in their ordinary

boy went around the

expected, he retorted that

to

he would

I

he understood by "going around" a a

if

would supply him with the he demurred, so that he might catch me either

and correct meaning, most monkey.

I

"to go around

his definition of

such

little

A man recently propounded to " A boy walks round a pole on

it

was not

man

To

because

you went

thing that it.

so,

this

I

made

in

the

could not go around

anything.

He all

then amended his definition by saying that the actual seeing

sides

was not

essential,

but you went in such a

xx

way

that,

given

INTRODUCTION sight,

you could see

was suggested

that

man who had been

shut

Upon which

sides.

all

consequently you could not walk around a

it

And so on. The whole thing is amusingly stupid, up in a box and if at the start you, very properly, decline to admit any but a simple and correct definition of "to go around" there !

no puzzle

is

and you prevent an

left,

and often heated,

idle,

argument.

When

you have grasped your conditions always see

simplify them, for a lot of confusion

if

you cannot

Many

got rid of in this way.

is

people are puzzled over the old question of the man who, while " Brothers and sisters have I none, but pointing at a portrait, says,

man s

that

father

" that

is

my "

my

father

s

father

son

s

What

son."

bear to the speaker

in the picture

"

must be either

statement simplified myself,"

over

this

and

it

is

thus nothing

was obviously

question by the hour

There are mysteries

little

" or

my

brother."

" it is

more

clearly

" than,

The

myself."

That man

s

father

Yet people

his son s portrait.

man

by saying

fight

!

have never

that

been solved

Let us consider a few

branches of Puzzledom.

numbers

simplify

"

myself

But, since the speaker has no brother,

is

relation did the

Here you

?

in

in the

many

world

of

things the conditions of which a child can understand,

Everybody has heard the though the greatest minds cannot master. " It is as hard as squaring a circle," though many people remark, have a very hazy notion

of

what

it

means.

If

you have a

circle of

given diameter and wish to find the side of a square that shall contain exactly the

same

squaring the

circle.

we it

area,

you are confronted with the problem

Well,

it

can get an answer near enough for

is

all

practical purposes) because

not possible to say in exact numbers

diameter to the circumference.

But

has been proved to be impossible, for to

perform a certain

feat,

of

cannot be done with exactitude (though

it is it is

what

is

the ratio of the

only in recent times that

but quite another to prove that xxi

it

one thing not to be able it

cannot be

INTRODUCTION done.

a square. there

is

can never measure exactly

The

to

this,

my

readers

quite easy,

and there

is

You

in

square of the of

doing

has been squares

and we before

it,

finally

a magic square

way

of

we

of nine cells

Then

of

to

is

so that

all

itself

the

add up 15. It is for we do not count

to

it,

Now 1

we

if

wish to make a

6, there are just

880

different

recent

years.

the 25 numbers,

But

to 25,

1

This

how many magic nobody knows,

extend our knowledge in certain directions

But

it is

may be formed

surprising to find of

one particular

the bordered square, in which the inner square

magic.

And

I

have shown

how

this

number

once doubled by merely converting every bordered square rule

into a

non-bordered one.

vain attempts have been made to construct a magic square " " is called a knight s tour over the chess-board, numbering

each square that the knight it

1

74,240 such squares

by a simple by what

6 numbers,

proved

restricted kind only

at

doing

can hope to solve the puzzle. 1

The numbers

is.

cells,

by merely turning round the

a mirror.

in

it

which way you

it

again not counting reversals and reflections.

have

shall

might

of the diagonals will

only one

may be formed with

that exactly

may be

1

can have

a square of nine

as different the arrangements obtained

square and reflecting

we

but then you can never say exactly

know what

columns and rows and each

ways

side,

both ways.

it

9 can be arranged

magic

of

the length of that

is

once suggest that

will at

the length of the side.

but you cannot have

All 1

on every

say an exact foot, and then construct our

first,

Yes, you can do

square.

numbers what

simple person

take our diagonal

like,

foot

the distance from corner to corner staring you in the face,

diagonal.

is

numbers the diagonal

in

you have a window pane exactly a

If

yet you can never say in exact

what

their time in trying to

circle.

we

Again,

now waste

uninstructed cranks

Only

square the

visits

in succession,

1 ,

2, 3, 4, etc.,

and

has been done with the exception of the two diagonals, which so xxii

INTRODUCTION far

have baffled

all

But

efforts.

it

is

not certain

that

it

cannot

be done. the contents

Though

the

of

entirely original, will not,

prove unwelcome

I

trust,

received.

The

puzzles are of

volume are

present

some very few old

friends will

in the

new

it

is

the main

be found, but these

dress that they have

every degree of

varied in character that perhaps

in

not too

difficulty

much

to

and so

hope

every true puzzle lover will find ample material to interest possibly instruct.

In

some

cases

I

full

I

solutions

and proofs been given

the book greatly increased.

advantages, for out his

own

it

in

would have had

And

Had

Even

the

the case of every puzzle, to

be omitted, or the

the plan that

I

size of

have adopted has

leaves scope for the mathematical enthusiast to

analyses.

of

have reluctantly

obliged to restrict myself to giving the bare answers.

either half the problems

and

have dealt with the methods

solution at considerable length, but at other times felt

that

in those cases

where

I

its

work

have given a

general formula for the solution of a puzzle, he will find great interest in verifying

it

for himself.

A

CHANCE-GATHERED company of Thomas a Becket at

shrine of Saint

Tabard

later called the

Inn,

pilgrims on their

way

to the

Canterbury, met at the old

Talbot, in South wark and the host

proposed that they should beguile the ride by each telling a tale to his fellow-pilgrims. This we all know was the origin of the " " immortal Canterbury Tales of our great fourteenth-century poet, Unfortunately, the tales were never completed,

Geoffrey Chaucer.

why the quaint and curious "Canterbury Puzzles," devised and propounded by the same body of pilgrims,

and perhaps

that

is

by the poet s pen. This is greatly to be " who, as Leland tells us, was an ingenious mathematician," and the author of a learned treatise on the astrolabe, was peculiarly fitted for the propounding of problems. In presenting

were not

also recorded

regretted, since Chaucer,

for the

first

time some of these old-world posers,

explain the singular manner in which they at once,

proceed an opportunity certainly far

I

will not stop to

came into my

possession, but

without unnecessary preamble, to give

of solving

more

them and

difficult

testing their quality.

puzzles extant, but difficulty

my

readers

There are and interest

are two qualities of puzzledom that do not necessarily go together.

1

.

The Reves Puzzle.

a wily man and something of a scholar. As " There was no auditor could of him win and " The poet also noticed there could no man bring him in arrear."

The Reve was

Chaucer

"

tells

us,

"

ever he rode the hindermost of the route." This he did that he might the better, without interruption, work out the fanciful that

1

B

THE CANTERBURY PUZZLES problems and ideas pilgrims

that:

were topping

passed through

his active brain.

When the

a wayside tavern, a number of cheeses of

at

varying sizes caught his alert eye, and calling for four stools he told the company that he would show them a puzzle of his own that

would keep them amused during their rest. He then placed eight cheeses of graduating sizes on one of the end stools, the smallest " This cheese being at the top, as clearly shown in the illustration. " that I did once set before my fellow towns is a riddle," quoth he,

men at Baldeswell, that is in Norfolk, and, by no man among them that could rede it aright. full

easy, for

all

that

I

do desire

is

that

Saint Joce, there

And

by the moving

yet of

it is

was

withal

one cheese

unto another, ye shall remove all the cheeses to the stool at the other end without ever putting any cheese on one at a time

that

least

is

from one

smaller than

number

of

stool

To him

itself.

moves

that

that will perform this feat in the

be possible

will

the best that our good host can provide."

the fewest possible moves,

with 21 cheeses,

is

first

with

8,

then with

an interesting recreation.

2

I

To

give a draught of solve this puzzle in 1

0,

and afterwards

THE CANTERBURY PUZZLES The Pardoner

2.

s

Puzzle.

"

The gentle Pardoner, that straight was come from the court of Rome/ begged to be excused, but the company would not spare him. "

and

Friends

fellow

" pilgrims," said he,

of

a truth the riddle that

have made thing, but

that

is it

have been able

I

I

but a poor is the best to

Blame my lack knowledge of such

devise. of

matters

your

if

it

be not

But

liking."

to his

invention

was very well

received.

He produced

the accompanying plan

and

said that

it

repre

sented sixty-four towns

through which he had to pass during some of his pilgrimages, and the lines connecting them were roads. He explained that the puzzle was to start from the large black town and visit all the other towns once, and once only, in fifteen straight pilgrimages. Try to trace the route in fifteen straight lines with your pencil. You may end where you like, but note that the apparent omission of a little road at the

bottom

is

intentional, as

it

seems that

it

was impossible

to

go

that way. 3.

The

The Millers Puzzle.

the company aside and showed them were standing as depicted in the sketch. " while that I do set Now, hearken all and some," said he, And mark ye, my ye the riddle of the nine sacks of flour. lords and masters, that there be single sacks on the outside, pairs next unto them, and three together in the middle thereof. By Saint Benedict, it doth so happen that if we do but multiply the pair, 28, by the single one, 7, the answer is 96, which is of a truth the 3 B 2 nine "

Miller

next

took

sacks of flour that

1

THE CANTERBURY PUZZLES number shown by the

sacks in the middle.

Yet

it

be not true that

the other pair, 34, when so multiplied by its neighbour, 5, will also make 96. Wherefore I do beg you, gentle sirs, so to place anew 1

the nine sacks with as

thus multiplied by middle.*

As

its

little

single

trouble as possible that each pair

neighbour

shall

make

the

number

when

in

the

the Miller has stipulated in effect that as few bags as

possible shall be moved, there is only one answer which everybody should be able to solve.

4.

The Knight

s

to this puzzle,

Puzzle.

This worthy man was, as Chaucer tells us, "a very perfect, " and In many a noble army had he been At

gentle knight,"

:

mortal battles had he been fifteen." His shield, as he is seen " " it to the company at the Tabard in the illustration, was, in

showing

THE CANTERBURY PUZZLES " the peculiar language of the heralds, argent, semee of roses, gules," which means that on a white ground red roses were scattered or is sown by the hand. When this Knight was called " This riddle a propound a puzzle, he said to the company,

strewn, as seed

on

to

wight did ask of

me when

that

fought with the lord of Palatine

I

hand take a piece of chalk and learn how many perfect squares thou canst make with one of the against the heathen in Turkey.

In thy

The

eighty-seven roses at each corner thereof."

reader

may

find

it

an interesting problem to count the number of squares that may be formed on the shield by uniting four roses.

5._ The Wife of Bath The

Wife

frolicsome

when

of Bath,

s

Riddles.

called

company, protested that she had no aptitude that her fourth husband had had a liking

remembered one " pilgrims.

of his riddles

Why

a bung

is

barrel like unto another

hath

to favour the

them and she

for

be new

that might

that

upon

for such things, but

to her fellow

been made

fast

a

in

" that

just falling out of

a barrel

bung company promptly answered this easy conundrum, the lady went on to say that when she was one day seated sewing in her " private chamber her son entered. Upon receiving," saith she, " the parental command, Depart, my son, and do not disturb me

As

is

?

the

*

!

he did

and

reply,

until

I

am,

of a truth, thy son, but thou art not

me how

thou hast shown

this

may be

This perplexed the company a good deal, but the reader

much

I

it

shall not is

my mother," go

forth.

not likely to give

difficulty.

6.

Perhaps no puzzle

The Host of the

whole

s

Puzzle.

collection caused

more

jollity

or

entertaining than that produced by the Host of " He the who Tabard," accompanied the party all the way. " called the pilgrims together and spoke as follows merry masters all, now that it be my turn to give your brains a twist,

was found more

:

I

will

full

show ye a

bent.

And

little

My

piece of craft that will try your wits to their it is but a simple matter when the

yet methinks

5

THE CANTERBURY PUZZLES Here be a cask of fine London ale, and doing of it is made clear. my hands do I hold two measures one of five pints, and the

in

other of three pints.

Pray show how

true pint into each of the measures."

it

is

Of

possible for

course,

me

no other

to put a

vessel or

be used, and no marking of the measures is allowed. little problem and a fascinating one. good many Yet it can persons to-day will find it a by no means easy task, be done. article It

is

to

A

a knotty

is

7.

The

The Clerk of Oxenford s Puzzle.

and thoughtful clerk of Oxenford, of whom it is Every farthing that his friends e er lent, In books and learning was it always spent," was prevailed upon to give his " companions a puzzle. He said, Ofttimes of late have I given much silent

recorded that

"

thought to the study of those strange talismans to ward off the plague and such evils, that are yclept magic squares, and the secret of such is very deep and the number of such squares truly great. But the small riddle that I did make yester eve for the purpose of

things

this

company

is

not so hard that any

6

may

not find

it

out with a

THE CANTERBURY PUZZLES little

patience."

He then

duced the square shown illustration and said that desired so to cut

pro

in the it

was

into four

it

pieces (by cuts along the lines) that they would fit together again and form a perfect magic square, in which the four col

umns, the four rows, and the

two long diagonals should add up 34. It will be found that this

is

a

just sufficiently

puzzle for

most people

The. Tapisers Puzzle.

8.

Then came forward tapestry,

easy

s tastes.

who

the Tapiser,

was, of course, a maker of

and must not be confounded with a

tapster,

who draws and

ale.

sells

He

of tapestry,

produced a beautiful piece

chequered pattern, as shown

in the

"

diagram.

worked

in

This piece

a simple

of tapestry,

>

X*

I



s

fb " sirs,"

and

I

quoth he,

hath one hundred and sixty-nine small squares,

do desire you

to

tell

me

the manner of cutting the tapestry

7

THE CANTERBURY PUZZLES fit together and make one whole piece shape of a perfect square. " Moreover, since there be divers ways of so doing, I do wish to know that way wherein two of the pieces shall together contain as much

into tnree pieces that shall in

as possible of the rich fabric."

clear that the Tapiser intended

It is

made

the cuts to be

along the lines dividing the squares only, and, as the material was not both sides alike, no piece may be reversed,

but care must be observed that

the chequered pattern matches

properly.

The Carpenter

9.

The

s

Puzzle.

Carpenter produced the carved wooden pillar that he is seen illustration, wherein the knight is propounding his

holding in the

knotty problem to the goodly "

There dwelleth

in

company (No. 4), and spoke as follows London a certain scholar that is :

the city of

learned in astrology and other strange arts. Some few days gone he did bring unto me a piece of wood that had three feet in length, one

and one

foot in breadth

and made

and did desire that it be carved do now behold. Also did he you

foot in depth,

into the pillar that

wood

promise certain payment for every cubic inch of

by the carving thereof. " I did at first weigh the block and found

Now

thirty

pounds, whereas the

Of

a truth

to

say

pillar

doth

of

the

three

away

truly to contain

now weigh

but twenty pounds. one cubic foot (which is

have therefore cut away

I

one-third)

it

cut

cubic

feet

of

the

block,

but

may not thus be fairly made by weight, since the heart of the block may be heavier, or How then may perchance may be more light, than the outside. I with ease satisfy the scholar as to the quantity of wood that hath this scholar

withal doth hold that payment

"

been cut away it

is

This

?

at first sight looks a difficult question,

so absurdly simple that the

should be "

known

to

but

method employed by the carpenter

everybody to-day,

for

it

is

a very useful

little

wrinkle/* 10.

Chaucer

says of the Squire

"

of pilgrims,

The Puzzle of the Squires Yeoman. s

Yeoman, who formed one

a forester was he truly as

8

I

guess,"

and

of his party tells

us that

THE CANTERBURY PUZZLES "

His arrows drooped not with feathers low

;

And

in his

hand he

When a halt was made one day at a wayside bare a mighty bow." " inn, bearing the old sign of the Chequers, this yeoman consented to give the company an exhibition of his skill. Selecting nine good " Mark ye, good sirs, how that I shall shoot these arrows, he said, nine arrows in such manner that each of them shall lodge in the *

middle of one of

the

squares

be upon the

that

sign

of

the

Chequers, and yet of a truth shall no arrow be in line with any The diagram will show exactly how he did this, other arrow." and no two arrows will be found in line, horizontally, vertically, or

"

Here Then the Yeoman said Remove three of the arrows each to one

diagonally. ye.

:

then of

is

its

squares, so that the nine shall yet be so placed that

may be

in

with another."

line

meant one that

By

a riddle for

neighbouring

none thereof

a "neighbouring square"

is

adjoins, either laterally or diagonally.

\\.-TheNunsPuzzle. " I

trow there be not one among ye," quoth the Nun, on a later " that doth not know that many monks do oft pass the

occasion,

time in play at certain games, albeit they be not lawful for them. These games, such as cards and the game of chess, do they cunningly hide from the abbot

s

eye by putting them away

9

in holes

THE CANTERBURY PUZZLES that they

have cut out

their

upon she do likewise

?

of the

very hearts of great books that be

nun therefore be greatly blamed if show a little riddle game, that we do

Shall the

shelves. I

will

sometimes play among ourselves be away."

The Nun illustration.

when

the good abbess doth hap to

then produced the eighteen cards that are shown in the She explained that the puzzle was so to arrange the

cards in a pack, that by placing the uppermost one on the table, placing the next one at the bottom of the pack, the next one on the

table,

on the

the next at the bottom of the pack, and so on, until " table, the eighteen cards shall then read

all

are

CANTERBURY

PILGRIMS."

Of course each card must be placed on the table the immediate right of the one that preceded it. It is easy enough if you work backwards, but the reader should try to arrive to

at the

required

order without

doing

this,

or

using

any actual

cards. 12.

Of the Merchant the man withal." He was

The Merchant

s

" poet writes, thoughtful,

full

Puzzle.

Forsooth he was a worthy of schemes, and a good

" His reasons spake he eke full solemnly, manipulator of figures. Sounding alway the increase of his winning." One morning when

they were on the road, the Knight and the Squire, who were riding beside him, reminded the Merchant that he had not yet propounded the puzzle that he owed the company. He thereupon " Be it so ? Here then is a riddle in numbers that I will set said, before this merry

be

company when next we do make a

thirty of us in all riding over the

may ride one and

one, in

common

what they do 10

call

this

halt.

morn.

the single

file,

There

Truly or

we

two and

THE CANTERBURY PUZZLES two, or three and three, or five and five, or six and six, or ten and and fifteen, or all thirty in a row. In no other way may

ten, or fifteen

we

be no lack of equal numbers in the rows. a party of pilgrims were able to thus ride in as many as sixty-four

ride so that there

Now,

different

Prithee tell ways. in the company."

have been smallest

number

of

me how many there must perforce The Merchant clearly required the the

sixty-four

rich of excellence.

Discreet

persons that could so ride in

ways. 1

The

3.

Sergeant of the

The.

Man

of Law

s

Puzzle.

"

Law was

full

He

was a very busy man, but He was like many of us to-day, "he seemed busier than he was." talking one evening of prisons and prisoners, and at length made the " And that which I have been saying doth following remarks forsooth call to my mind that this morn I bethought me of a riddle he was, and

of great reverence."

:

on I will now He then produced a slip of vellum, put forth." " Here," which was drawn the curious plan that is now given. " saith he, be nine dungeons, with a prisoner in every dungeon save These prisoners be numbered in order, 7, 5, one, which is empty. that

11

THE CANTERBURY PUZZLES 6, 8, 2,

moves

One

1,

4, 3,

and

I

desire to

know how

as possible, put themselves in the order

may move

prisoner

that doth

happen

to

at a time along the

they can, in as few 1

2, 3, 4, 5, 6, 7, 8.

,

passage to the dungeon

be empty, but never, on pain

of death,

may two

"

How may it be done ? any dungeon at the same time. If the reader makes a rough plan on a sheet of paper and uses numbered counters he will find it an interesting pastime to arrange men be

in

the prisoners in the fewest possible moves.

As

than one vacant dungeon at a time to be may be recorded in this simple way, 3 2

moved

14.

The Weaver s Puzzle.

When the Weaver brought out a square piece of beautiful cloth,

daintily

ered

and

embroid

with

lions

castles, as

de

picted in the

illus

the

pil

tration,

grims disputed among themselves as to the

meaning

of these

ments.

orna

The

Knight, however,

who was skilled

1

in

12

there

6,

is

never more

into,

and so

the moves on.

THE CANTERBURY PUZZLES heraldry, explained that they castles

borne

in

were probably derived from the lions and III., the King of Castile and

the arms of Ferdinand

In this Leon, whose daughter was the first wife of our Edward I. he was undoubtedly correct. The puzzle that the Weaver proposed " Let us, for the nonce, see/* saith he, "if there be any was this. of the

company

that can

into four several pieces,

show how

each

this

piece of cloth

same

of the

may be

cut

and shape, and each not recorded that anybody size

piece bearing a lion and a castle."

It is

mastered

quite possible of solution in a

this

puzzle, though

No

satisfactory manner. a castle.

15.

We

cut

is

it

may

TTje

pass through any part of a lion or

Cook

s

Muzzle.

that there was a cook among the company, and his " were no doubt at times in great request, For he could roast and seethe, and broil and fry, And make a mortress and well bake a find

services

One night when the pilgrims were seated at a country hostelry, about to begin their repast, the cook presented himself at the head of the table that was presided over by the Franklin, and said, pie."

"

Listen awhile

my

by Saint Moden

I do ask ye a riddle, and cannot answer myself withal.

masters, while that it

is

one that

I

13

THE CANTERBURY PUZZLES There be eleven pilgrims seated at this board on which is set a warden pie and a venison pasty, each of which may truly be divided into four parts and no more. Now, mark ye, five out of the eleven pilgrims can eat the pie, but will not touch the pasty, while four will

away from

eat the pasty but turn

do remain be able and there any that can

Franklin

that

tell

me

in

may choose whom he

reader that

if

he

is

halidame,

is

different ways the good " will serve ? I will just caution the

when he

of forty, as all the

Clerk of Oxenford

down

By my

how many

not careful he will find,

he has made a mistake

exception of the

Moreover, the two that

the pie.

willing to eat of either.

who

sees the answer,

company did with the

got

it

right

by accident,

a

wrong figure. Strange to say, while the company perplexed their wits about In the midst this riddle the cook played upon them a merry jest. through putting

of their deep thinking and hot dispute what should the cunning knave do but stealthily take away both the pie and the pasty. Then, when hunger made them desire to go on with the repast, finding

there was nought upon the table, they called clamorously for the cook. "

My

riddle,

with

I

masters," he explained,

" seeing you

were

so deep set in the

did take them to the next room where others did eat them ere they

relish

and cheese

had grown

There be

cold.

excellent bread

in the pantry."

16.

The Sompnour,

The Sompnour

s

Puzzle.

Summoner, who, according to Chaucer, joined whose duty was to summon In later times he delinquents to appear in ecclesiastical courts. became known as the apparitor. Our particular individual was a " somewhat quaint, though worthy, man. He was a gentle hireling better fellow should a man not find/* and a kind In order that or

the party of pilgrims, was an officer

;

the reader

A

may understand

his

appearance

in

the picture,

it

must be

explained that his peculiar headgear is duly recorded by the poet. " garland had he set upon his head, As great as if it were for an

A

ale-stake."

14

THE CANTERBURY PUZZLES One

evening ten of the company stopped at a village inn and up for the night, but mine host could only accommodate five of them. The Sompnour suggested that they requested to be put

should draw lots, and as he had had experience in such matters in the summoning of juries and in other ways, he arranged the company in

a circle and proposed a

nature, his little plot

was

"

count out."

out and leave the ladies in possession. of

Bath a number and directed her

circle, in fell

was

afresh

He

the

next

person.

and selected

the count at herself. falling

in

As

will

whom

Wife

that

number

count then began misunderstood her

number eleven and

be found,

all fall

The

But the lady

mistake the

should

round and round the

a clockwise direction, and the person on

at

of a chivalrous

men

therefore gave the

to count

to immediately step out of the ring.

instructions

women

Being

so to arrange that the

this

resulted in

started all

the

out in turn instead of the men, for every eleventh

person withdrawn from the circle

is

15

a lady.

THE CANTERBURY PUZZLES "Of

was no fault of mine," said the Sompnour next " company, and herein is methinks a riddle. Can any day tell me what number the good Wife should have used withal, and at which pilgrim she should have begun her count so that no other than a truth

it

to the

the five is

point

men

the smallest

find

to

"

should have been counted out

number

Of

?

that will

the

course,

have the desired

effect.

The Shiftman

17.

Of

this

they were,

person

we

are told,

From Gothland

"He

to the

s

Puzzle.

knew

Cape

well

of

all

creek

in

Spain

\

the havens, as

Finisterre,

:

And

and

His barque

ycleped was the

dalen"

every

Brittany

The

Mag strange

puzzle in navigation that

he propounded was

as

follows.

"

.

%

%

4^ i

\

^

,

\

/

Here be a chart," " quoth the Shipman, of with the five islands, inhabitants of

do

trade.

my good

which

ship doth

over every one of courses

ten

OT

ye

sail

the

depicted

thereon, but never

MAC,DAltJ.

I

In each year

may

she pass along the same Is there any among the company who course twice in any year. can tell me in how many different ways I may direct the Magdalen s ten yearly voyages, always setting out from the same island 18.

?

The Mon^s Puzzle.

The Monk that went with the party was a great lover of sport. Of riding and of Greyhounds he had as swift as fowl of flight would he spare." cost no hunting for the hare Was all his love, for "

:

One

day he addressed the pilgrims 16

as follows

:

THE CANTERBURY PUZZLES "

There

a

is

though certes

some

wits of

my

though the one

may

Now,

place

number

of

is

kennels

in

matter that hath at times perplexed me greatly, no great weight, yet may it serve to try the

of

be cunning

in such things. Nine kennels have I and they be put in the form of a square, the middle I do never use, it not being of a useful

dogs,

the riddle

is

to find in

how many

my dogs dogs on every side of the square in

small diagrams

way

is

that

for the use of

nature.

little

it

show

all

four

different

ways

I

or any of the outside kennels so that the

ways

of

doing

may be

it,

just ten."

The

and though the fourth

Any merely a reversal of the third, it counts as different. may be left empty. This puzzle was evidently a variation of

the ancient one of the Abbess and her Nuns.

\9.The

Puzzle of the Prioress.

The Prioress, who went by the name of Eglantine, is best remembered on account of Chaucer s remark, "And French she spake full fair and properly, After the school of Stratford-atte-Bow, For French of Paris was to her unknow." But our puzzle has to do less with her character and education than with her dress. "And thereon hung a brooch of gold full sheen, On which was written

first

a crowned A."

It

is

17

with the brooch that

C

we

are

THE CANTERBURY PUZZLES concerned, for

when asked

company and

to the

said

showed

to give a puzzle she

"A

:

learned

this

jewel

man from Normandy

once give

me

this

did

brooch as

a charm, saying strange and mystic things anent it, how that

hath an

it

affinity for

the square, and such other

wise words that were too

But the good Chertsey did once

subtle for me.

Abbot tell

of

me

that the cross

be so cunningly cut pieces

that

they

may

into four will

join

and make a perfect square.

Though on my It is

recorded that

"

faith

I

know

not the manner of doing

it."

the pilgrims did find no answer to the riddle,

and the Clerk of Oxenford thought that the Prioress had been deceived in the matter thereof, whereupon the lady was sore vexed, though the gentle knight did flout and gibe at the poor clerk because of his lack of understanding over other of the riddles,

which did

fill

him with shame and make merry the company." 20.

The Puzzle of the Doctor of Physic.

This Doctor, learned though he was, for "In

him there was none

"He

knew

to the

more

like

To

all

this

world

to

speak of physic and of surgery," and

the cause of every malady," yet was he not indifferent " material side of life. Gold in physic is a cordial ;

Therefore he loved gold in special." The problem that the Doctor propounded to the assembled pilgrims was this. He produced two spherical phials, as

shown

in

one phial was exactly a foot

our

illustration,

and pointed out that and the other two

in circumference,

feet in circumference.

" I

do wish,"

" said the Doctor, addressing the

company,

to

have

the exact measures of two other phials, of a like shape but different in size, that may together contain just as much liquid as is contained

18

THE CANTERBURY PUZZLES

To

by these two." numbers is one

of the toughest nuts

the

of

thickness

find exact dimensions

the glass,

in

the smallest possible

have attempted. Of course and the neck and base, are to be I

ignored.

The Ploughman

21.

The Ploughman

of

and very good was

whom

he,

s

like

for simple

minds

but he

would

his,

show the good

"A

Chaucer remarked

worker true

Living in perfect peace and charity

"-

^

protested that riddles

were not

Puzzle.

pilgrims,

one that he had frequently heard if

they willed

it,

certain clever folk in his

>, \

own neighbourhood dis " cuss. The lord of the manor

in

the

Sussex whence

part I

hath a plantation of sixfair oak trees, and

teen

/

of

\&

">>

come

^

,

,- J

.

*^~

they be so set out that they make twelve rows with four trees in every row. Once on a time, a man of deep learning who happened to be travelling in those parts, did say that the sixteen trees might

19

c 2

THE CANTERBURY PUZZLES have been so planted, that they would make so many as straight rows, with four trees in every

me how

might be

this

The

be done."

to

the twelve rows.

"

A

fifteen

Can ye show

have doubted that twere possible shows one of many ways of forming

How

can

22.

The Franklin

We are

thereof.

Many

?

illustration

Franklin was in

row

this

we make

company

;

fifteen ?

s

Puzzle.

White was

his

beard as

is

by Chaucer that he was a great house " Without baked meat never was his holder and an epicure. Of fish and flesh, and that so plenteous, It snowed in his house.

the daisy."

told

of meat and drink, Of every dainty was a hospitable and generous man.

house

He

that

"

men His

could bethink."

table

dormant

in

alway Stood ready covered all throughout the day." At the repasts of the Pilgrims he usually presided at one of the tables, as we found him doing on the occasion when the cook propounded hall

his

his

problem day

One on him

to

of the at

two

an inn

pies. just outside

Canterbury, the company called

produce the puzzle required

whereupon he placed 3, up to 15, with the " 2^

of him,

numbered 1, on the table sixteen bottles " it will be one marked 0. Now, my masters," quoth he, fresh in your memories how that the good Clerk of Oxenford did show us a riddle touching what hath been called the magic square. Of a truth will I set before ye another that may seem to be somelast

20

THE CANTERBURY PUZZLES what

of a like kind, albeit there

Here be

set out sixteen bottles in

place them afresh

be

little

form

in

common

of a square,

betwixt them.

and

I pray you so form a magic square, adding up to But mark well that ye may not ways.

that they shall

thirty in all the ten straight

remove more than ten

from their present places, for This is a little puzzle that

of the bottles

therein layeth the subtlety of the riddle."

conveniently tried with sixteen

may be

23.

The Squire

s

numbered

counters.

Puzzle.

The young

Squire, twenty years of age, was the son accompanied him on the historic pilgrimage.

that

of the

He

Knight

was un

doubtedly what

we a

"

times

later

in

should

dandy,

call

for,

Embroidered was he as is a mead, All

full

of fresh flowers,

white and red. Singing he was or fluting day,

He

all

fresh as

month in

the

tion to

is

of

As will

the

was

as

the

May."

be seen illustra

No. 26,

while the

Hab

erdasher was propounding his problem of the triangle, this young Squire was standing in the background making a drawing of some " He could songs make and well indite, Joust and eke kind, for dance, and well portray and write." " The Kftight turned to him after a while and said,

My "son,

what

and the over which thou dost take so great pains withal ? " in one I how me I have might portray bethought Squire answered,

is

it

21

THE CANTERBURY PUZZLES only stroke a picture of our late sovereign lord King Edward the Tis a riddle to find Third, who hath been dead these ten years.

where the

who I

first

am

stroke doth begin

shall

show

it

unto

and where

me

will

I

Man

of

Law.

It

may be here remarked

pilgrimage set out from Southwark on the Third died in 1377. 24.

The

doth also end.

To him

able to present a facsimile of the original drawing,

was won by the

1

7th April,

1

387, and

which

that the

Edward

The Friars Puzzle.

was a merry fellow, with a sweet tongue and twinkling Courteous he was and lowly of service. There was a man

Friar

" eyes.

it

give the portraiture."

"

nowhere so virtuous." Yet he was the best beggar in all his house," and gave reasons why "Therefore instead of weeping and much 22

THE CANTERBURY PUZZLES *

must give silver to the needy friar. He went by the One day he produced four money bags and name of Hubert. " If the needy friar doth receive in alms five spake as follows hundred silver pennies, prithee tell in how many different ways they

Men

prayer,

:

may be placed made no

order

in

the four bags."

The good man

difference (so that the distribution 50,

explained that 1

00,

1

50,

200

would be the same as 100, 50, 200, 150, or 200, 50, 100, 150,) and one, two, or three bags may at any time be empty. 25.

The Parson was priest

I

The Parsons Puzzle.

a really devout and good man.

trow there nowhere

loved by

all

flock, to

whom

is."

"

A

better

His virtues and charity made him be

his

he presented his

with patience and

teaching

simplicity, first

"but

he followed

himself." Now, Chaucer

it

is

careful to

us that

tell

"Wide

was his parish, and houses far

asunder, But he neglected nought for ram or thunder/* and

it

is

with

his parochial

He

visitations

that

the

Parson

s

puzzle

actually

dealt.

through which a small river ran that joined the sea some hundreds of miles to the south. I give a facsimile of the plan. " Here, my worthy Pilgrims, is a strange riddle," quoth the " Behold how at the branching of the river is an island. Parson.

produced a plan

of part of his parish,

23

THE CANTERBURY PUZZLES this island doth stand my own poor parsonage, and ye may see the whereabouts of the village church. Mark ye, also, that

Upon all

there be eight bridges and no more over the river in

On my way

to

church

in the

doing thereof once and no more.

I

it is

my wont

to visit sundry of

do pass over every one

Can any

my parish. my flock, and

of the eight bridges

find the path, after this

of

ye manner, from the house to the church, without going out of the parish ? Nay, nay, my friends, I do never cross the river in any boat, neither

by swimming nor wading, nor do mole, nor

fly in

There

bridges."

I

go underground

the air as doth the eagle is

this curious journey.

a

way in which Can the reader

;

like

unto the

but only pass over by the

the Parson might have discover

it

At

?

first it

made seems

impossible, but the conditions offer a loophole.

26.

The Haberdasher s Puzzle.

made to induce the Haberdasher, who was propound a puzzle of some kind, but for a long time At last, at one of the Pilgrims stopping-places, without success. " he said that he would show them something that would put their

Many

attempts were

of the party, to

brains into a twist like unto a bell-rope."

he was

As

a matter of

fact,

on the company, for he was the puzzle that he set them. He

really playing off a practical joke

quite ignorant of any answer to produced a piece of cloth in the shape of a perfect equilateral " Be there any among triangle, as shown in the illustration, and said, in the of cloth I trow full wise true ? not. cutting Every man ye to his trade,

man from

and the scholar may learn from the

the fool.

Show

me, then,

if

ye can,

and the wise what manner this

varlet in

may be cut into four several pieces that may be make a perfect square." Now some of the more learned of the company found a way of But when they pressed the doing it in five pieces, but not in four. Haberdasher for the correct answer he was forced to admit, after much beating about the bush, that he knew no way of doing it " " in any number of pieces. By Saint Francis," saith he, any knave can make a riddle methmks, but it is for them that may piece of cloth

put together to

to rede

it

aright."

For

this

he narrowly escaped a sound beating.

24

THE CANTERBURY PUZZLES But the curious point of the puzzle is that I have found that may really be performed in so few as four pieces, and

the feat

without turning over any piece

method

when

doing this is subtle, but problem a most interesting one. of

27.

One

I

placing

them

together.

The

think the reader will find the

The Dyers Puzzle.

was a Dyer, but Chaucer tells us nothing Time after time the Tales being incomplete. company had pressed this individual to produce a puzzle of some The poor fellow tried his best to follow kind, but without effect. of the pilgrims

about him,

the

examples of his friends the Tapiser, the Weaver, and the Haberdasher, but the necessary idea would not come, rack his brains as he would. All things, however, come to those who the

wait

and persevere

and one morning he announced 25

in

a state

THE CANTERBURY PUZZLES of considerable excitement that

He

he had a poser to set before them. silk on which were embroidered

brought out a square piece of

a number of fleurs-de-lys in rows, as shown in our illustration. " " hearken anon unto my riddle. Lordings," said the Dyer, for which Since I was awakened at dawn by the crowing of cocks din may our host never thrive

have sought an answer by St. Bernard

I

thereto, but I

have found

it

There

not.

be sixty-and-four flowers-deluce, and the riddle is to

show how A

$V3

A

Vi

men

are alive and in hiding in the

again. "

Whose

That

was a

tall

is

is

the large foot

Lamson s, and

man,

just

over

district.

"

Just examine the prints

?

the small print

six feet,

is

Marsh

and Marsh was a

little

s.

Lamson

fellow."

" And yet you will find thought as much," said Melville. that Lamson takes a shorter stride than Marsh. Notice, also, the "

I

peculiarity that

treads

not

;

more on

but has

Because you

it

Marsh walks

heavily on his heels, while

Lamson

Nothing remarkable in that ? Perhaps occurred to you that Lamson walked behind Marsh ? his toes.

will find that

he sometimes treads over Marsh 73

s

foot-

THE CANTERBURY PUZZLES steps,

never find Marsh treading

will

though you

in

the steps of the

other."

"

Do

you suppose that the men walked backwards

in their

own

"

asked the inspector.

footprints ?

"

No

that

;

is

No

impossible.

some two hundred yards

two men could walk backwards

way

in that

with such exactitude.

You

where they have missed the print by even Nor do I suppose that Quite impossible.

will not find a single place

an eighth

of

an inch.

two men, hunted

as they were, could

have provided themselves with

flying-machines, balloons, or even parachutes.

over the

They

did not drop

cliff."

His Melville then explained how the men had got away. account proved to be quite correct, for it will be remembered that they were caught, hiding under some straw in a barn, within two

How

miles of the spot.

did they get

away from

the edge of the

cliff?

The Runaway Motor-Car.

64.

The

" little affair

of the

"

Runaway Motor-car

is

a good

illustra

how

a knowledge of some branch of puzzledom may be put to unexpected use. member of the Club, whose name I have tion of

A

at the

moment

of writing forgotten,

came

in

one night and said that

a friend of his was bicycling in Surrey on the previous day, when a motor-car came from behind, round a corner, at a terrific speed,

He was caught one of his wheels, and sent him flying in the road. badly knocked about, and fractured his left arm, while his machine was wrecked. unable to trace

The

motor-car was not stopped, and he had been

it.

There were two

witnesses to the accident, which

question the fault of the driver of the car.

Wadey, saw the whole car. She was positive and was

and

tried to

the

first

which need not be given, The other was a 1. the speed and dust.

figure

read on account of

other witness

was beyond

woman, a Mrs. take the number of the old

as to the letters,

certain also that

figures she failed to

The

thing,

An

was the

being an arithmetical genius, but

village simpleton, is

who

just

escapes

excessively stupid in everything else.

74

ADVENTURES OF THE PUZZLE CLUB He was

always working out sums in his head

is

that there

were

that when he multiplied the made the same figures, only

by 651 makes

number was no

1

in the

five figures first

two

order

he could say

1

last

three they

24 multiplied in which case the and he knew there

just as

5,624 (the same five figures), would have been 24,65

of the car in the

all

by the

figures

in different

and

;

number, and that he found

;

number. "

*

be easy enough

It will

known

facts

to find that car," said Russell.

The

are possibly sufficient to enable one to discover the

exact number.

You

numbers having the

must be a

see, there

limit to

the five-figure

by the simpleton. And as Mrs. Wadey states, the

peculiarity observed

these are further limited by the fact that,

number began with the

figure

1

We

.

have therefore to

find these

may conceivably happen only one such which case the thing is solved. But even if there are several cases, the owner of the actual car may easily be found." numbers.

number, "

that there

It

is

in

How

"

will

you manage

that ?

75

somebody asked.

THE CANTERBURY PUZZLES "

"

the method is quite obvious. Every owner except the one in

By

Surely," replied Russell,

the process of elimination. will be able to prove an think

it

case.

alibi.

fault

Yet, merely guessing offhand,

quite probable that there

is

only one

number

that

fits

I

the

We shall see."

was right, for that very night he sent the number by post, with the result that the runaway car was at once traced, and its Russell

owner,

who was

resulting from

himself driving,

his carelessness.

The

to

pay the the

mystery of Ravensdene Park, which tragic

cost of the

number

damages

of the car ?

The Mystery of Ravensdene Park-

65.

was a

had

What was

affair,

as

I

will

now

involved the assassination of

it

present,

Mr.

Cyril

Hastings at his country house a short distance from London. On February 7th, at p.m., there was a heavy fall of snow, it half lasted an hour, the ground was covered to a and, though only 1

1

1

6

depth

of

several

inches.

Mr. Hastings had been spending the

evening at the house of a neighbour, and left at midnight to walk home, taking the short route that lay through Ravensdene Park

A in the sketch-plan.

is, from D to he was found dead,

that

at the point indicated

76

But in the early morning by the star in our diagram,

ADVENTURES OF THE PUZZLE CLUB stabbed to the heart.

and the

footprints in the

All the seven gates were promptly closed, snow examined. These were fortunately

and the police obtained the following facts Mr. Hastings were very clear, straight from D There were the footprints of the to the spot where he was found. Ravensdene butler who retired to bed five minutes before midnight from E to EE. There were the footprints of the gamekeeper Other footprints showed that one to his lodge at AA. from individual had come in at gate B and left at gate BB, while another very

distinct,

The

:

footprints of

A

had entered by gate C and left at gate CC. Only these five persons had entered the park since the fall of snow. Now, it was a very foggy night, and some of these pedes trians had consequently taken circuitous routes, but it was particularly Of this the police noticed that no track ever crossed another track. were absolutely certain, but they stupidly omitted to make a sketch of the various routes before the snow had melted and utterly effaced them.

The who at

mystery was brought before the members of the Puzzle Club, once set themselves the task of solving it. Was it possible Was it the Butler ? Or to discover who committed the crime ? the gamekeeper

BB

?

Or

the

Or the man who came ? man who went in at C and

vided themselves with diagrams

in at

B

left at

and went out

CC

?

at

They pro

sketch-plans, like the one

we have

reproduced, which simplified the real form of Ravensdene Park without destroying the necessary conditions of the problem.

Our

friends then

proceeded to trace out the route

77

of

each person,

THE CANTERBURY PUZZLES accordance with the positive statements of the police that we have It was soon evident that, as no path ever crossed another, given. some of the pedestrians must have lost their way considerably in the

in

But when the tracks were recorded

fog.

had no

difficulty in

in all possible

deciding on the assassin

route

s

ways, they and, as the

;

knew whose footprints this route represented, an arrest man s conviction. Can our readers discover whether A, B, C, or E committed the

police luckily

was made deed key

that led to the

Just trace out the route of each of the four persons,

?

to the

mystery

The Buried Treasure.

66.

The problem

A

and the

will reveal itself.

of the

Buried Treasure was

of

quite a different

young fellow named

Dawkins, just home from Australia, was introduced to the club by one of the members, in order that he might relate an extraordinary stroke of luck that

character.

he had experienced "down under," as the circumstances involved the solution of a poser that could not fail to interest all lovers of After the club dinner, Dawkins was asked to tell puzzle problems. his story,

"

I

which he

have

did, to the following effect

told you, gentlemen, that

I

:

was very much down on my

I had gone out to Australia to try to retrieve my fortunes, but had met with no success, and the future was looking very dark. I One hot summer day I was, in fact, beginning to feel desperate. happened to be seated in a Melbourne wineshop, when two fellows entered, and engaged in conversation. They thought I was asleep, but I assure you I was very wide awake.

luck.

*

could find the right field/ said one man, the treasure would be mine and as the original owner left no heir, I have If

only

I

;

much

it as anybody else/ would you proceed ? asked the other. The document that fell into my hands Well, it is like this states clearly that the field is square, and that the treasure is buried in it at a point exactly two furlongs from one corner, three furlongs from the next corner, and four furlongs from the next corner to that.

as

right to

How

:

You

see, the

worst of

it is

that nearly

78

all

the

fields in

the district are

ADVENTURES OF THE PUZZLE CLUB square If

and

;

only

I

doubt whether there are two of exactly the same size. field I could soon discover it, and, by

I

knew

the size of the

taking these simple measurements, quickly secure the treasure/

But you would not know which corner

which

My over

;

nor

dear chap, that only means eight spots at the most to dig

and

bet that

"

to start from,

direction to go to the next corner.

as the

wouldn

t

paper says that the treasure take

me

long.

is

three feet deep, you

"

Now,

I gentlemen," continued Dawkins, happen to be a bit of a mathematician ; and, hearing the conversation, I saw at once that for a spot to be exactly two, three, and four furlongs from suc

cessive corners of a square, the square must be of a particular area.

You can t get such measurements to meet at one point in any square you choose. They can only happen in a field of one size, and that is just what these men never I will leave you the suspected. puzzle of

working out

just

what

that area

is.

79

THE CANTERBURY PUZZLES "

Well,

when

I

found the

discovering the field

And

conversation.

would have treasure was a luck

enabled

me

itself,

it,

I

man had

did not need to

the third spot

I

substantial sum, for

let

make

tried it

I

the eight digs,

was the

often smile

shows

when

I

me home and

I

saying

:

think of that poor If

only

I

knew

the

while he has placed the treasure safe in my own tried to find the man, to make him some compensation

size of the field

possession.

life

as

The

signs of being a

*

fellow going about for the rest of his

for,

right one.

has brought

to start in a business that already

particularly lucrative one.

I was not long in out the district in the

size of the field,

for the

!

anonymously, but without success. Perhaps he stood of the money while it has saved me from ruin."

in little

need

Could the reader have discovered the required area of the field details overheard in the wineshop ? It is an elegant little puzzle, and furnishes another example of the practical utility, on unexpected occasions, of a knowledge of the art of problemfrom those

solving.

80

THE PROFESSOR S PUZZLES "

"

"

Why,

here

is

the Professor

exclaimed Grigsby.

!

make him show us some new puzzles." It was Christmas Eve, and the

club

was

We

ll

deserted.

nearly

Only Grigsby, Hawkhurst, and myself, of all the members, seemed to be detained in town over the season of mirth and minceThe man, however, who had just entered was a welcome pies. " The Professor of Puzzles/* as we had addition to our number. nicknamed him, was very popular at the club, and when, as on the present occasion, things got a little slow, his arrival was a positive blessing.

He

was a man

inclined to

be

middle age,

of

He

cynical.

had

cheery and kind-hearted, but all

his

dabbled

life

in

puzzles,

problems, and enigmas of every kind, and what the Professor didn t know about these matters was admittedly not worth knowing. His puzzles always "

You

in," said *

I

are the

own, and this was mainly them up in palatable form. others that we were hoping would drop

had a charm

because he was so happy

man

of all

Hawkhurst.

"

of their

in dishing

Have you

got anything

have always something new," was the

feigned conceit

for the Professor

was

Where do you

get

all

"

?

reply,

really a modest

simply glutted with ideas." "

"

new

uttered with "

man

"

"

m

"

your notions

?

I

asked.

Everywhere, anywhere, during all my waking Indeed, two or three of my best puzzles have come

my

I

moments. to

me

in

dreams."

Then

" all

the good ideas are not used up

Certainly not.

And

all

?

the old puzzles are capable of improve81 G

THE CANTERBURY PUZZLES ment, embellishment, and

extension.

These were constructed

squares.

Era, and introduced into Europe

when I

am

in

Take, India

for

example, magic the Christian

before

about the fourteenth

numbers one eight ways.

problem

if

to

nine

But you

in

a

will see

square that will add up fifteen in it can be developed into quite a new

you use coins instead of numbers/* a rough diagram, and placed a crown and a

He made two

century,

they were supposed to possess certain magical properties that afraid they have since lost. Any child can arrange the

florin in

of the divisions, as indicated in the illustration.

"

*

Now," he coins

in

the

continued,

place the fewest possible current English of the three

seven empty divisions, so that each

67.

The Coinage, Puzzle.

columns, three rows, and two diagonals shall add up fifteen Of course, no division may be without at least one coin, shillings. and no two divisions may contain the same value."

82

THE PROFESSOR S PUZZLES "

But

how

can the coins

"

"

asked Grigsby.

affect the question ?

That you will find out when you approach the solution." " " I shall do it with numbers first," said Hawkhurst, and then substitute coins."

Five minutes

can

however, he exclaimed,

later,

help getting the 2 in a corner.

t

May

"

its

"

Hang

the florin be

it

all

!

I

moved from

present position ? " Certainly not." " Then I give it up."

But Grigsby and time,

so the

I

and then went on with

Now,

his chat.

The Postage Stamps Puzzles.

68.

"

we would work at it another Hawkhurst the solution privately,

decided that

Professor showed

instead of coins

we

substitute

ll

Take

postage-stamps.

them being all of different Stick two of them in one division that the square shall this time add

ten current English stamps, nine of

and the tenth a and one in each of the

values,

duplicate. others, so

up ninepence in the eight directions as before." " " Here you are cried Grigsby, after he had been for a few minutes on the back of an envelope. !

The Professor smiled indulgently. " Are you sure that there is a current "

the value of threepence-halfpenny

scribbling

English postage-stamp of

?

"

"

For the life of me, I don t know. Isn t there ? " There That s just like the Professor," put in Hawkhurst. You never know when you have never was such a tricky man. got to the bottom of his puzzles. Just when you make sure you have found a solution, he trips you up over some little point you "

never thought of." "

When

you have done much better one for you. every three divisions in a

stamps as It is

" that," said

Stick line

the Professor,

here

shall

add up

you choose, so long as they are

alike,

all

a

using as

many

of different values.

a hard nut."

83

is

English postage stamps so that

2 G

THE CANTERBURY PUZZLES 69.

The Frogs and Tumblers.

"

"

What do you think of these ? The Professor brought from his frogs, snails, lizards,

capacious pockets a

and other creatures

very grotesque in form and

of

number

of

Japanese manufacture

While we were

brilliant in colour.

-j >% ^3

* .

****,

N%

-

^

(

l^~^.

*

*

f

_^

**

x

\V

\ t

v

them he asked the waiter to place sixty-four tumblers table. When these had been brought and arranged in the form of a square, as shown in the illustration, he placed eight

looking at

on the club of the

"

little

Now

"

green frogs on the glasses as shown. " he said, you see these tumblers form eight horizontal

84

THE PROFESSOR S PUZZLES and eight

vertical

and

lines,

if

ways) there are twenty-six other all

these forty-two

lines,

you look

will find

you

at

them diagonally (both

you run your eye along no two frogs are anywhere in

lines.

If

a line." "

The puzzle is this. Three of the frogs are supposed to jump from their present position to three vacant glasses, so that in their new What are the relative positions still no two frogs shall be in a line. jumps made ? " I suppose " I

"

"

began Hawkhurst.

know what you

are going to ask," anticipated the Professor.

the frogs do not exchange positions, but each of the three to a glass that was not previously occupied." jumps " " But surely there must be scores of solutions ? I said. " I shall be very glad if you can find them," replied the Professor " I only know of one or rather two, counting a with a dry smile.

"No,

reversal,

which

occurs

in

consequence

of

the

position

being

symmetrical."

70.

For some time feat allotted to

not give

away

we

tried to

them, and his

Romeo and Juliet. make

failed.

solution,

those

The

little

reptiles

perform the

Professor, however,

would

but said he would instead introduce

little thing that is childishly simple when you have once seen but cannot be mastered by everybody at the very first attempt. " " Waiter he called again. "Just take away these glasses,

to us a it,

!

please,

"

and bring the chessboards."

"

you are not going hope to goodness," exclaimed Grigsby, White to show us some of those awful chess problems of yours. The to mate Black in 427 moves without moving his pieces. " bishop rooks the king, and pawns his Giuoco Piano in half a jiff. " You see these two snails. They are No, it is not chess. Romeo and Juliet. Juliet is on her balcony waiting the arrival of her love, but Romeo has been dining and forgets, for the life of him, The squares represent sixty-four houses, the number of her house. and the amorous swain visits every house once and only once before 85 I

THE CANTERBURY PUZZLES reaching his beloved.

Now, make him do

The

this

with the fewest

can move up, down, and across the Mark his track with this piece of board and through the diagonals. possible turnings.

snail

chalk." "

Seems easy enough," said Grigsby, running the chalk along the " Look That does it." squares. !

"

"

Yes," said the Professor

;

Romeo

has got there,

it

is

true,

and visited every square once, and only once, but you have made him turn nineteen times, and that is not doing the trick in the fewest turns possible."

Hawkhurst

curiously enough, hit on the solution at once, and the this was just one of those puzzles that a

Professor remarked that

person might solve at a glance or not master

86

in six

months.

THE PROFESSOR S PUZZLES 71

.

Romeo s Second

"It was a sheer stroke "

added.

Here

a

is

of

much

Journey.

luck on your part, Hawkhurst," he

easier

puzzle, because

it

is

capable of

more systematic analysis yet it may just happen that you will not do it in an hour. Put Romeo on a white square and make him ;

crawl

into

other

every

white

once

square

with

the

fewest

This time a white square may be visited twice, must never pass a second time through the same corner

possible turnings.

but the snail

of a square nor ever enter the black squares."

"

"

May No

he leave the board

"

asked Grigsby.

for refreshments ?

*

he

;

is

not allowed out until he has performed his

The Frogs

72.

Who Would

a-

feat.

Wooing Go.

While we were vainly attempting to solve this puzzle, the Professor arranged on the table ten of the frogs in two rows, as they will be found in the illustration. "

"

That seems

" It is

a

little

entertaining,"

puzzle

I

I

made a year

few people who have seen

it.

What

said.

It is

ago,

" is

and a

The

called

?

it

favourite with the

Frogs

Who Would

Four of them are supposed to go a-wooing, and have each made a jump upon the table, they are in such a position that they form five straight rows with four frogs in

a- Wooing

Go.

after the four

every row."

"What s few minutes

"

that later

?

asked Hawkhurst.

he exclaimed,

"

"

How s

87

I

think "

this ?

I

can do that."

A

THE CANTERBURY PUZZLES "

They form

six of

"

only four rows instead of

five,

and you have moved

them," explained the Professor.

Hawkhurst,"

said Grigsby, severely,

Here you

the solution at a glance.

are

!

you are a duffer. I see These two jump on their

comrades* backs." "

No, no/* admonished the Professor. "That is not allowed. I distinctly said that the jumps were to be made upon the table. Sometimes it passes the wit of man to so word the conditions of a problem that the quibbler will not persuade himself that he has found a flaw through which the solution may be mastered by a child of five.**

After for

some

we had

been vainly puzzling with these batrachian

lovers

time, the Professor revealed his secret.

The

Professor gathered up his Japanese reptiles and wished us three who good-night with the usual seasonable compliments.

We

remained had one more pipe together, and then also left for our Each believes that the other two racked their respective homes. brains over

Professor

s

unanimous " solve

we

Christmas

in

puzzles, but in declaring

really

the determined attempt to master

when we

next met at the club

that those puzzles

had not had time

to look

which we had at,**

mastered after an enormous amount of labour first

glance directly

we

got home.**

88

we were

"

all

failed to

while those

we had

the

we had

seen at the

MISCELLANEOUS PUZZLES The Game of Kayles.

73.

Nearly though

in

improved.

all

of our

many

most popular games are of very ancient origin, have been considerably developed and

cases they

Kayles

parent of our modern

word q miles was a and was undoubtedly the Kayle-pins were not con-

derived from the French

great favourite in the fourteenth century,

game

of ninepins.

any particular number, and they were and set up in a straight row. At first they were knocked down by a club that was thrown at them from a distance, which at once suggests the origin of the fined

in

generally

those

made

days

to

of a conical shape,

89

THE CANTERBURY PUZZLES "

"

shying at cocoanuts

pastime of

that

is

to-day so popular on Bank Then the players

Holidays on Hampstead Heath and elsewhere. introduced balls, as an improvement on the club. In the illustration

we

get a picture of

some

of our fourteenth-

century ancestors playing at kayle-pins in this manner. Now, I will introduce to my readers a new game of

parlour

can be played across the table without any pre You simply place in a straight row thirteen whatever. paration dominoes, chess-pawns, draughtsmen, counters, coins, or beans kayle-pins, that

all close together, and then remove the second one, anything will do as shown in the picture.

It is assumed that the ancient players had become so expert that they could always knock down any single kayle-pin, or any two They therefore altered the kayle-pins that stood close together.

was agreed it was the winner.

game, and last

pin

that the player

Therefore, in playing our table-game,

knock down with your

who knocked down all

you have

to

do

the

is

to

fingers, or take away, any single kayle-pin or

two adjoining kayle-pins, playing alternately until one of the two I think it will be found players makes the last capture, and so wins. a fascinating little game, and I will show the secret of winning. Remember that the second kayle-pin must be removed before you begin to play, and that if you knock down two at once those two must be close together, because in the real game the ball could not do more than this.

The Broken Chessboard.

74.

There

is

afterwards

a story of Prince Henry, son of William the Conqueror, Henry I., that is so frequently recorded in the old

chronicles that

the

incident

it

is

is

Conqueror, published "

The following version of Hayward s Life of William the

doubtless authentic.

taken in

Towards the end

from

1613 of

his

:

reigne he appointed his two sonnes

Robert and Henry, with joynt authoritie, governours of Normandie the one to suppresse either the insolence or levitie of the other. ;

90

MISCELLANEOUS PUZZLES These went together

to visit the

French king lying

at

Constance

:

where, entertaining the time with varietie of disports, Henry played with Louis, then Daulphine of France, at chesse, and did win of him very much.

"

Hereat Louis beganne

growe warme in words, and was The great impatience of the one respected by Henry. and the small forbearance of the other did strike in the end such a heat between them that Louis threw the chessmen at Henry s

therein

to

little

face.

"

Henry

again stroke Louis with the chessboord,

91

drew blood

THE CANTERBURY PUZZLES with the blowe, and had presently slain him upon the place had he not been stayed by his brother Robert. " Hereupon they presently went to horse, and their spurres claimed so good haste as they recovered Pontoise, albeit they were sharply pursued by the French."

Now, tradition on this point not trustworthy says that the chessboard broke into the thirteen fragments shown in our illustra It will be seen that there are twelve pieces, all different in tion. shape, each containing five squares, and one

squares only. thus have

We

the puzzle

make a

is

all

piece of four

little

the sixty-four squares of the chessboard, and

simply to cut

them out and

fit

them

together, so as to

The

perfect board properly chequered.

pieces

may be

"squared" paper, and, if mounted on cardboard, they will form a source of perpetual amusement in the easily cut out of a sheet of

home. If

you succeed

in constructing the chessboard, but

the arrangement, you will find

disposed to attack it. Prince Henry himself, with

it

just as

do not record

puzzling the next time you

feel

found

it

75.

Inside 1

2

all

his skill

and

would have

learning,

an amusing pastime.

feet in

The Spider and

the Fly.

a rectangular room, measuring 30 feet in length and width and height, a spider is at a point on the middle of

one ^

end

of the

from the

and a wall,

3O

as

1

foot

at

A,

on the opposite foot from the floor in

fly is 1

the centre, as

What

walls,

ceiling,

is

shown

at

B.

the shortest distance

that the spider must crawl in

-ft.

order to reach the

fly,

which

remains stationary ? Of course the spider never drops or uses web, but crawls fairly.

92

its

MISCELLANEOUS PUZZLES The Perplexed Cellarman.

76.

Here very little

a

is

little

puzzle

culled

from the

traditions of

an old

West of England. Abbot Francis, it seems, was a man and his methods of equity extended to those worthy in the

monastery

;

acts of charity for

The Abbot,

which he was noted

moreover, had a

for miles round.

taste

fine

in

wines.

On

one

occasion he sent for the cellarman, and complained that a particular bottling

was not

"

Pray

to his palate.

me, Brother John,

tell

how much

of this

wine thou

didst

bottle withal."

"

A

dozen

fair

in the small,"

been drunk "

So be

two dozen

in

large bottles,

replied the cellarman,

my "

lord abbot,

whereof

and the

five of

like

each have

in the refectory."

it.

There be three

bottles

varlets waiting at the gate.

be given unto them, both

93

full

Let the

and empty, and see

THE CANTERBURY PUZZLES that the dole

be

fairly

made, so that no man receive more wine than

another, nor any difference in bottles."

Poor John returned to his cellar, taking the three men with him, and then his task began to perplex him. Of full bottles he had seven large and seven small, and of empty bottles five large and five How was he to make the small, as shown in the illustration. required equitable division ? He divided the bottles into three groups in several ways that at first sight seemed to be quite fair, since two small bottles held just the same quantity of wine as one large one. But the large bottles themselves, when empty, were not worth two small ones.

Hence number

the abbot

of bottles of

order that each

s

each

man must

take

away

the same

size.

Finally, the cellarman had to consult one of the monks who was good at puzzles of this kind, and who showed him how the thing was done. Can you find out just how the distribution was made ?

77.

A

good

Making a

dissection puzzle in so

perhaps the reader diagram represents a

rarity, so

The

piece of bunting, and

it

required to cut

two

it

into

will

Flag.

few

as

two

pieces

be interested

is

in the

rather a following.

is

pieces (without any waste) that will

fit

together and

form a flag,

perfectly square with the four roses

symmetrically placed. This

would be easy enough if it were not for the four roses, as

we

to cut

should merely have

from

A

to B,

insert the piece at the

to cut through

puzzle.

Of

any

course

and bottom

of the flag.

of the roses,

we make no

and therein

But lies

allowance for

"

we

are not allowed

the difficulty of the turnings."

MISCELLANEOUS PUZZLES 78. In the illustration

Catching the Hogs.

Hendrick and Katriin are seen engaged

in the

exhilarating sport of attempting the capture of a couple of hogs.

Why did they Strange as puzzle

game

it

fail ?

may

that

I

seem, a complete answer

will

now

afforded in the

is

little

explain.

Copy the simple diagram on a conveniently large sheet of card board or paper, and use four marked counters to represent the Dutchman, his wife, and the two hogs.

At the beginning of the game these must be placed on the squares on which they are shown. One player represents Hendrick and The first player moves the Dutch Katriin, and the other the hogs. man and

his wife

one square each

in

95

any direction (but not diagonally), I

THE CANTERBURY PUZZLES and then the second player moves both pigs one square each and so on, in turns, until Hendrick catches one hog and Katriin the ;

other.

This you but this

is

would be absurdly easy what Dutch pigs will not do.

will find

just

79.

This I

a

is

know) a

game

moved

the hogs

first,

The Thirty -one Game.

that used to be (and

favourite

if

means

may be

to this day, for aught

of swindling

employed by cardsharpers at racecourses and in railway-carriages. As, on its own merits, however, the I

it

game is particularly interesting, make no apology for presenting

will

my The

to

readers.

down

cardsharper lays

twenty-four cards shown in the tration,

and

invites the innocent

farer to try his luck or

which

them can

of

the illus

way

by seeing

skill

score thirty-

first

one, or drive his opponent beyond, in the following

One

manner "

a 2, and counts player turns

two

down

:

down

player turns

" ;

a card, say the second

a card, say a 5,

and, adding this to the score, counts " " the first player turns down seven ;

another card, say a 1, and counts " " and so the play proceeds eight ;

alternately until

one

"

the

Now, first

the question

is,

in

thirty-one,"

and

of

order to win, should you turn

;

scores

down

card, or courteously request your opponent to do so

how should you conduct your play ? The reader will "Oh, that is easy enough. You must play first, and 3

them

so wins.

?

the

And

perhaps say turn

down

:

a

then, whatever your opponent does, he cannot stop your making

96

MISCELLANEOUS PUZZLES ten, or

stop your making seventeen, twenty-four,

You have

thirty-one.

and the winning

only to secure these numbers to win."

knowledge which is such a dangerous hands of the sharper. thing, places you " You play 3, and the sharper plays 4 and counts seven" you " " ten the sharper turns down 3 and scores play 3 and count But

this

and

is

just

that

little

in the

it

;

;

"

"

"

"

the sharper plays a you play 4 and count seventeen 4 and counts twenty-one" you play 3 and make your "twenty-four." Now the sharper plays the last 4 and scores " twenty-eight." thirteen

;

;

"

;

You all

look in vain for another 3 with which to win, for they are

turned

down

"

"

thirty-one

You

!

So you

thus see that your

utterly,

are compelled either to

method

of certainly

by what may be called the

give the key to the game, showing

like to find

him make the

method

down

winning breaks

of exhaustion."

how you may first

I

will

always win but I or second you may ;

:

out for yourself.

it

The Chinese Railways.

80.

Our

"

here say whether you must play

will not

let

or to go yourself beyond, and so lose the game.

illustration

shows the plan

Chinese

of a

city

protected by

Five European Powers were scheming pentagonal and clamouring for a concession to run a railway to the place and at last one of the Emperor s fortifications.

;

more

brilliant advisers said,

"

Let every one of them " So have a concession !

the

Celestial

officials

were kept busy ar

ranging

the

letters in

different

and

indicate

where each belonging the

line

The

details.

show

the diagram

the

the

Government

to of

nationalities,

not only just line

that

must enter the line

city,

but also where the station

must be located.

As

it

one company must never cross the

representatives

of

the

various

97

countries

was agreed line of

that

another,

concerned

H

were

THE CANTERBURY PUZZLES engaged so many weeks in trying meantime a change

that in the

to find a solution to the problem, in

the Chinese Government was

Take your brought about, and the whole scheme fell through. to A, B to B, pencil, and trace out the route for the line

A

C

to C,

and so

on, without ever allowing

or pass through another

company

This

line to cross

another

s station.

The Eight Clowns.

81.

illustration represents

Continent.

one

a troupe of clowns I once saw on the of the numbers 1 to 9 on his

Each clown bore one

After going through body. the usual tumbling, juggling,

and other rally

antics, they gene concluded with a few

curious

little

numerical

tricks,

which was the rapid formation of a number of one

of

It

magic squares. to

me

that

failed to

occurred

clown No.

if

appear

(as

1

happens

in the illustration), this last

item

of

their

performance

The might not be so easy. reader is asked to discover

how

these eight clowns

may

arrange themselves in the form of a square (one place being vacant), so that every one of the three columns, three rows, and each of the two diagonals

add up the same. the square, but it is No.

The

shall

82.

Once upon The

wizard.

1

vacant place

that must

may be

at

any part

of

be absent.

The Wizard s Arithmetic.

a time a knight went to consult a certain famous had to do with an affair of the heart, but

interview

98

MISCELLANEOUS PUZZLES man of magic had foretold the most favourable issues, and concocted a love-potion that was certain to help his cause, the con

after the

versation drifted on to occult subjects generally. * " And art thou learned also in the magic of numbers ? asked the " Show me but one sample of thy wit in these matters." knight.

The

old wizard took five blocks bearing numbers, and placed shelf, apparently at random, so that they stood in

them on a

the order, 41096, in

as

shown

hands an 8 and a

his

3,

our

in

He

illustration.

and held them together

then took

to

form the

number 83. "

" Sir knight,

number "

me," said the wizard,

into the other in thy

Nay, set out

tell

mind

"

"

of a truth," the

upon the

task

canst thou multiply one

?

good knight replied. with pen and scrip."

99

I

should need to

H 2

THE CANTERBURY PUZZLES "

Yet mark ye how

right easy a thing

Araby, who knoweth " philosophy of numbers lore of far

all

it is

man

to a

learned in the

the magic that

hid in the

is

!

The wizard 8

at the

simply placed the 3 next to the 4 on the shelf, and the It will be found that this gives the answer other end.

quite correctly

3410968.

Very

curious,

is

it

How

not?

many

other two-figure multipliers can you find that will produce the same You may place just as many blocks as you like on the shelf, effect ?

bearing any figures you choose.

83.

The Ribbon Problem.

If we take the ribbon by the ends and pull it out straight, we This number has the have the number 0588235294117647. if

peculiarity that,

multiply of the 4,

we

get

2, 3,

or 9,

8,

7,

exactly

same number circle, starting

different

we

by any one

numbers, 6,

5,

it

in

the the

from a

place.

For

example, multiply by 4,

and the product

is

2352941176470588, which

starts

from the

dart in the circle.

So,

we multiply by 3, we get the same re

if

sult starting

from the

Now,

the puzzle

star. is

to place a different

arrangement

on the ribbon that only the

will

produce

and the 7 appearing

similar results at the

be removed.

100

when

of figures

so multiplied,

ends of the ribbon must not

MISCELLANEOUS PUZZLES 84.

The Japanese Ladies

aria the

Three Japanese ladies possessed a square ancestral carpet of con siderable intrinsic value, but treasured also as an interesting heirloom in

the family.

of

it,

They decided

to cut

it

up and make three square rugs

own house. way would be for

so that each should possess a share in her

One

lady suggested that the simplest

her to

take a smaller share than the other two, because then the carpet need not be cut into more than four pieces.

There are three easy ways of doing this, which I will leave the reader for the present the amusement of finding for himself, merely saying that if you suppose the carpet to be nine feet square, then one

may take a piece two feet square whole, another a two feet square in two pieces, and the third a square foot whole. But this generous offer would not for a moment be entertained by lady

101

THE CANTERBURY PUZZLES the other two

sis-tors,

wht> msfeed that the square carpet should be mat of exactly the same size.

so cut chat each saould get- a square

Now, found

it

according to the best Western authorities they would have necessary to cut the carpet into seven pieces, but a corre

spondent

few

in

Tokio assures

as six pieces,

me

that the legend

and he wants

to

is

that they did

know whether such

it

in as

a thing

is

possible.

Yes

;

can be done.

it

Can you equal size

cut out the six pieces that will form three square mats of

?

85.

The English Tour.

This puzzle has to do with railway routes, and of

much travelling should prove

useful.

The map

in

these days

England shows

of

twenty-four

towns,

connected by a system

A

of railways.

dent

at

marked of

the

A at map

the top

proposes

to visit every

the

resi

the town

one

of

towns once and

only once, and to finish

up his tour at Z. This would be easy enough if he were able to cut across country by road, as well as by but he is not. rail, How does he per form the

feat ?

Take

your pencil and, starting from A, pass from town to town,

making a dot end at Z.

in

the towns you have visited, and see

102

if

you can

MISCELLANEOUS PUZZLES 86.

Captain Longbow and the Bears.

That eminent and more or less veracious traveller, Captain Longbow, has a great grievance with the public. He claims that during a recent expedition in Arctic regions he actually reached the North Pole, but cannot induce anybody to believe him. Of course,

the difficulty in such cases

is

to

produce proof, but he avers that

when

they succeed in accomplishing the same feat, He says that when he got there he will find evidence on the spot. future travellers

saw a bear going round and round the top of the pole (which he declares is a pole), evidently perplexed by the peculiar fact that no matter in what direction he looked it was always due south. Captain Longbow put an end to the bear s meditations by shooting him, and afterwards impaling him, in the manner shown in the

103

THE CANTERBURY PUZZLES illustration, as

evidence for future travellers to which

the

have

I

alluded.

When

the Captain got one hundred miles south on his return he had a little experience that is somewhat puzzling. He journey was surprised one morning on looking down from an elevation

no fewer than eleven bears

to see

in his

immediate

But

vicinity.

what astonished him more than anything else was the curious fact that they had so placed themselves that there were seven rows of bears, with four bears in every row. Whether or not this was the result of pure accident he cannot say, but such a thing might If the reader tries to make eleven dots on a sheet have happened. paper so that there shall be seven rows of dots with four dots in every row, he will find some difficulty, but the captain s alleged of

grouping of the bears they were arranged

is

quite possible.

Can you

discover

how

The Chifu-Chemulpo Puzzle.

87.

Here

is

?

a puzzle that

was

London

recently on sale in the

shops.

an engine and eight cars. The represents a military tram to reverse the so that is in shall be the order cars, they puzzle It

8,

7,

6, 5, 4,

engine

left,

3,

as at

2,

1,

first,

instead of

1,2,

on the side

3,

track.

4,

5, 6,

Do

with the

8,

7,

this

in

the fewest

possible moves.

Every

time the engine or a car

is

main

moved from

or vice-versa,

a

the

to the side track,

move

it

counts

each car

for

or engine passed over

one

Moves as

along the main track are not counted.

the

points.

extremity,

is just room to pass 7 on to the side track, run 8 and bring down 7 again or you can put as many as five The or four and the engine, on the siding at the same time.

shown, there to 6,

up

cars,

cars

;

move without

" to

of

With 8 at the

try to

do

it

in

the aid of the engine.

20 moves."

How 104

The

purchaser

many do you

is

require

?

invited

MISCELLANEOUS PUZZLES The Eccentric Market-woman.

88.

Mrs. Covey, the most

who

eccentric

keeps a

women

poultry farm in Surrey,

little

Her manner

ever met.

I

is

one

of

of

doing business is always original, and sometimes quite weird and wonderful. In our illustration she is seen explaining to a few of her choice friends

how

she had disposed of her day

s

it

is

such an improvement on

senting

it

to

my

She

readers.

that

it

I

we

are

have no

related that she

a certain number of eggs to market.

She had

eggs.

got the idea from an old puzzle with which

She

customer, and gave him half an egg over.

all

evidently

familiar, but

hesitation in pre

had

She next

day taken them to one

that

sold half of

sold a third of

and gave a third of an egg over. She then sold a fourth of the remainder, and gave a fourth of an egg over. Finally, she disposed of a fifth of the remainder, and gave a fifth of an

what she had

egg over.

left,

Then what

thirteen of her friends. all

she had

And,

left

she divided equally among had not throughout

strange to say, she

these transactions broken a single egg.

find the smallest possible

have taken to market.

number

Can you

Now,

say

105

how many

the puzzle

is

to

Mrs. Covey could

of eggs that ?

THE CANTERBURY PUZZLES The Primrose Puzzle.

89. Select the

name

of

contains eight letters.

any flower that you think suitable, and that Touch one of the primroses with your pencil

and jump over one

of

the adjoining flowers to another,

on which

mark

you letter

Then

the

vacant

flower,

again jump over in

first

your word. touch another

of

another

and one

direction,

and write down the second

Con

letter.

tinue this (taking the letters in their

order)

letters

original

word can be

correctly read

until

proper all

the

have been

written down, and the round the garland. You must

always touch an unoccupied flower, but the flower jumped over may be occupied or not. The name of a tree may also be selected.

Only English words may be 90.

used.

The Round Table.

Seven friends named Adams, Brooks, Cater, Dobson, Edwards, Fry and Green, were spending fifteen days together at the seaside, and they had a round breakfast table at the hotel all to themselves. It was agreed that no man should ever sit down twice with the same two neighbours. As they can be seated, under these condi But could tions, in just fifteen ways the plan was quite practicable. The the reader have prepared an arrangement for every sitting ? hotel proprietor was asked to draw up a scheme, but he miserably failed.

106

MISCELLANEOUS PUZZLES The Five Tea-Tins.

91.

Sometimes people

will

speak of mere counting as one of the but on occasions, as I shall show,

simplest operations in the world it is

far

from easy.

;

Sometimes the labour can be diminished by the

little artifices sometimes it is practically impossible to make the required enumeration without having a very clear head indeed.

use of

;

An

ordinary child, buying twelve postage-stamps, will almost in when he sees there are four along one side and three " Four times three are twelve," while his tiny along the other,

stinctively say,

brother will count them

If the child s rows, "1,2, 3, 4," &c. add up the numbers 2, 3, up to 50, she will most probably make a long addition sum of the fifty numbers, while her husband (more used to arithmetical operations) will see at

mother has occasion

all in

to

1

,

a glance that by joining the numbers at the extremes there are = 1,275. But his smart son of 25 pairs of 51 therefore, 25 x 51 ;

twenty may go one better and

" say,

Why

multiply by 25

?

Just

add two O s to the 5 and divide by 4, 1

and there you are!"

A tea has

merchant

five

tea-

tin

boxes

of

shape,

which

cubical

he

keeps on his counter in a row, as shown in

our

illustration.

Every box has a picture on each of its

six

sides,

so

there are thirty pic in

tures

all

;

but

one picture on on No. 4 are repeated on No. 4, and two other pictures There are, therefore, only twenty-seven differrepeated on No. 3. 107

No.

1

is

THE CANTERBURY PUZZLES The owner always keeps No. 1 at one end of the row, ent pictures. and never allows Nos. 3 and 5 to be put side by side. The

tradesman

s

customer, having obtained this information, thinks

in how many ways the boxes may be on the so counter that the order of the five pictures in arranged front shall never be twice alike. He found the making of the count a tough little nut. Can you work out the answer without getting it

a good puzzle to

work out

Of course, two similar pictures your brain into a tangle ? in a row, as it is all a question of their order. 92.

The

The Four Porkers.

four pigs are so placed, each in a separate

mmmmM^MM

WMM

may be

IMHM

*

MMHOMMHMM

sty, that

One

eVer Y

although f the

thirty-six sties

straight

line

is

in

a

(either vertic

horizontally, ally,

or diagonally),

with

at least

one

the pigs, yet no pig in line

In

of is

with another.

how many

differ

ways may the four pigs be placed ent

to

these con

fulfil

If you turn page round you

ditions ? this

more ar rangements, and if get

7

front of a mirror

you get four more.

" f*

three

you turn

These are not

to

it

round

in

be counted

as different arrangements.

93.

The

TTie

Number

Blocks.

children in the illustration have found that a large

very interesting and instructive puzzles

108

may be made

number of number

out of

MISCELLANEOUS PUZZLES blocks

;

that

is,

blocks bearing the ten digits, or Arabic figures

2, 3, 4, 5, 6, 7, 8, 9,

and

The

0.

particular puzzle that they

1,

have

been amusing themselves with is to divide the blocks into two groups of five and then so arrange them in the form of two multiplication sums that one product of possible solutions

is

shall

The number

be the same as the other.

very considerable, but they have

arrangement that gives the smallest possible product. multiplied by

You

will

2

find

6,970, and 6,970 multiplied by

is

hit

on that

Thus, 3,485 1

is

the same.

it

quite impossible to

get any smaller re sult.

Now, my puzzle is

to find the largest

possible result. Divide the blocks into

any two groups

of five that

you like, and arrange them to form two multi plication sums that shall

produce the

same product, and the largest amount That is possible. all, and yet it is a nut that requires some cracking. allowed, nor any tricks whatever.

Of The

course, fractions

puzzle

is

are

not

quite interesting

have given it. Perhaps should be added that the multipliers may contain two figures.

enough

in the simple

form

Here

is

a

probably

little

which

I

it

Foxes and Geese.

94.

will

in

puzzle of the moving counters class that my readers Make a diagram of any convenient

find entertaining.

size similar to that

shown

in

our

illustration,

109

and provide

six

counters

THE CANTERBURY PUZZLES three

marked

to represent

Place the geese on the discs

numbered

Now,

10, 11,

and

the puzzle

is

1

1

foxes ,

2,

and three to represent geese. 3, and the foxes on the discs

and

2. this.

By moving one

at

a time, fox and

goose alternately, along a straight line from one disc to the next one, and 2 try to get the foxes on 1,2, and 3, and the geese on 0, 1

1

that

1 ,

1

make them

is,

exchange places in the fewest possi

ble moves.

But you must be careful never to let

a fox and goose get within reach of

each other, or there

will be trouble. This

rule,

find,

prevents you

will

you

moving the fox from

1

1

on the

first

move, as on either 4 or 6 he would be within reach a

goose.

It

of

also

If you prevents your moving a fox from 10 to 9, or from 12 to 7. play 10 to 5, then your next move may be 2 to 9 with a goose, which you could not have played if the fox had not previously gone

perhaps unnecessary to say that only one fox, or one Now, what is the goose, can be on a disc at the same time.

from

10.

smallest

It is

number

change places

of

moves necessary

95.

Here

is

to

make the

foxes and geese

?

Robinson Crusoe

s

Table.

a curious extract from Robinson Crusoe

s

diary.

It

is

not to be found in the modern editions of the Adventures, and

110

MISCELLANEOUS PUZZLES omitted in the old.

is

This has always seemed

to

me

to

be a

pity.

"

The

day in the morning, the wind having abated during went down to the shore hoping to find a typewriter and other useful things washed up from the wreck of the ship, but all that fell in my way was a piece of timber with many holes in it. My man Friday had many times said that we stood sadly in need of a square table for our afternoon tea, and I bethought me how this And since during piece of wood might be used for that purpose. third

the night,

I

the long time that

now me I

had

Friday

been

ith

\

was not wanting

to

lay a foundation of useful

knowledge

in his

him

mind,

told

it

wish to

from the tim

table

ber

I

was my make the

that

had found,

I

without there being any holes in the top thereof. "

Friday was

sadly put to

how

say

this

more

be,

it

to

might

especially

should consist of no more than two pieces joined to gether, but I taught him how it could be done in such a way that the table might be as large as was possible, though, to be as

I

said

sure,

I

it

was amused when he

they stop up Now, the of

wood with it

My fall

nation

do much

better

;

"

through/

gives the exact proportions of the piece did Robinson the positions of the fifteen holes.

illustration

Crusoe make the that

said,

holes, so pieces sugars not

How

largest possible square table-top in

should not have any holes in it Ill

?

two

pieces,

so

THE CANTERBURY PUZZLES The Fifteen Orchards.

96.

In the county of Devon, where the cider comes from, fifteen of the inhabitants of a village are imbued with an excellent spirit of friendly rivalry,

experiment a trees.

Some

and a few years ago they decided

little

to settle

by actual

difference of opinion as to the cultivation of apple

said they

want plenty

of light

and

while others

air,

ought to be planted pretty closely, in order that they might get shade and protection from cold winds. So they agreed to plant a lot of young trees, a different number in each

stoutly maintained that they

order

in

orchard, to

compare

results.

One man had single

a

his

another

trees,

three

another trees,

and

in

another had

field,

two had

tree

trees,

had four

another

five,

so on, the last

man having as many as fifteen trees

in

his

little

orchard. Last year

a very curious re sult was found to

have come about.

Each individuals discovered that every tree in his

the same

number

of apples.

But,

own

of the fifteen

orchard bore exactly

what was stranger

still,

on com

paring notes they found that the total gathered in every allotment was almost the same. In fact, if the man with eleven trees had given one apple to the man who had seven trees, and the man with fourteen trees had given three each to the men with nine and thirteen trees, they

Now,

the puzzle

would is

all

have had exactly the same. how many apples each would have

to discover

112

MISCELLANEOUS PUZZLES had (the same carried out.

in

It

is

every case) quite easy

97.

When

that

if

if

you

little

set to

distribution

work

had been

in the right

way.

The Perplexed Plumber.

paid a visit to Peckham recently I found everybody has happened to Sam Solders, the plumber?" He seemed to be in a bad way, and his wife was seriously anxious about I

"

What

asking,

the state of his mind. for

As

he had

fitted

up a hot-water apparatus

me

some^years ago which did not lead to an explosion for three months

least

at

(and then only damaged the com plexion of

one

the cook

follow

I

ers),

said

of

had consid

erable

him. "

s

regard for

There he

is,"

Mrs. Solders,

when

I

called "

how he s been three weeks.

hardly thing,

to

That

inquire.

s

for

He

eats

any and takes no

rest, whilst his busi

ness

is

that

I

so neglected

don

children. figuring,

into

t

know what

All day long

and tearing

going to happen to me and the five and night too there he is, figuring and

is

his hair like

a

mad

thing.

worrying

It s

me

an early grave."

I persuaded Mr. Solders to explain matters to me. It seems that he had received an order from a customer to make two rectangular

zinc cisterns, one with a top

was

to hold exactly

and the other without a

1,000 cubic feet of water

113

when

top.

Each

filled to I

the

THE CANTERBURY PUZZLES The

was

to be a certain amount per cistern, including Mr. Solders is a thrifty man, so he naturally desired to make the two cisterns of such dimensions that the smallest This was the little possible quantity of metal should be required. question that was so worrying him.

brim.

price

cost of labour.

Can my

Now

readers

ingenious

dimensions

the

find

of

the

most

economical cistern with a top, and also the exact proportions of such a cistern without a top, each to hold ,000 cubic feet of water ? By " " economical is meant the method that requires the smallest possible 1

quantity of

would

call

No

metal.

"

out of his dilemma.

me would

margin need be allowed for what ladies

*

turnings.

be useful

I

He

shall

says

to others in

:

show how I helped Mr. Solders " That little wrinkle you gave

my

trade."

The Nelson Column.

98.

During a Nelson celebration standing in Trafalgar

I

was

Square with a

He

friend of puzzling proclivities.

some time been gazing at the column in an abstracted way, and seemed quite unconscious of the

had

for

casual remarks that

I

addressed to

him.

What are you dreaming about ? I

said at "

"

last.

Two

" feet

he murmured. "

"

Somebody

s

Trilbys

?

I

in

quired.

" "

Five times round

Two

What

feet,

five

times

round

!

"

on earth are you saying ? " Wait a minute," he said, begin

ning to figure something out on the now detected that he was in the throes I back of an envelope. of producing a new problem of some sort, for I well knew his methods of working at these things. 114

MISCELLANEOUS PUZZLES "

Here you

interesting

"

are

little

!

"

he suddenly exclaimed.

The

puzzle.

That

s it

A very

!

height of the shaft of the Nelson

column being 200 feet, and its circumference 6 feet 8 inches, it is wreathed in a spiral garland which passes round it exactly five times. 1

What really

is

the length of the garland

?

It

looks rather

difficult,

but

is

remarkably easy."

He

was right. The puzzle is quite easy if properly attacked. Of course the height and circumference are not correct, but chosen for the purposes of the puzzle.

The

artist

has also intentionally drawn

the cylindrical shaft of the column of equal circumference through If it were tapering, the puzzle would be more difficult. out.

99.

A country baker in the next village,

the baker.

The Two Errand Boys. boy with a message same time the butcher

sent off his

and

at the

to the butcher

sent his

boy

One

to pass at a spot

ten minutes at

to

ran faster than the other, and they were seen 720 yards from the baker s shop. Each stopped his destination and then started on the return

115

I

2

THE CANTERBURY PUZZLES when it was found that they passed each other at a spot 400 yards from the butcher s. How far apart are the two trades men s shops ? Of course each boy went at a uniform pace

journey,

throughout. 100.

On

Ramsgate Sands.

the

Thirteen youngsters were seen

in

dancing

a

The

puzzle

is

this.

ring

on

the

"

Round the many rings may they

Apparently they were playing

Ramsgate sands. Mulberry Bush."

How

form without any child ever taking twice the hand of any other That is, no child may ever have a child right hand or left ? second time the same neighbour. 101.

Pope has

The Three Motor-Cars.

told us that

canst not see,"

and

able coincidences

all

certainly little

chance

we

all

is

One

of

come

across remark

things against the probability of the occur

rence of which the odds are immense

ment.

but "direction which thou

occasionally

the three motor

men

that in

fill

us with bewilder

the illustration has just

happened on one of these queer coincidences. He is pointing out to his two friends that the three numbers on their cars contain all to 9 and 0, and, what is more remarkable, that if the the figures numbers on the first and second cars are multiplied together they 116 1

MISCELLANEOUS PUZZLES will

make

the

26,910 contain of

two,

three

the same peculiarity. the

numbers have

number

is

third

car.

That

78, 345,

is,

and

the ten figures, and 78 multiplied by 345 makes the reader will be able to find many similar sets of

all

Now,

26,910.

numbers

number on the

and

five

But there this

is

figures

one

additional

a multiple of the

first.

set,

only, in

have which

the

second

respectively

and one

peculiarity

that

In other words,

if

that

345 could

be divided by 78 without a remainder, the numbers on the cars

would themselves fulfil this extra condition. What are the three numbers that we want ? Remember that they must have two, three, and five figures respectively.

A

102.

Can you shall

Reversible

Magic Square.

construct a square of sixteen different numbers so that

be magic (that

is,

adding up alike 117

in the four rows, four

it

columns

THE CANTERBURY PUZZLES and two not

diagonals),

You

?

whether you turn the diagram upside down or

3, 4 or 5, as these figures will not 6 may become a 9 when reversed, a 9 a 6, a 7 a 2, The 8 and will read the same both ways.

must not use a

reverse, but a

and a 2 a

7.

Remember

that the constant must not

1 ,

103.

be changed by the

reversal.

The Tube Railway.

The above diagram fare

is

is the plan of an underground railway. The uniform for any distance, so long as you do not go twice

along any portion of

the line during the same

a

Now

journey.

certain

passenger,

with plenty of time on his hands, goes daily

from

many

A

to

How

F.

different routes

are there from which

he may

select ?

For

example, he can take the short direct route, A, B, C, D, E, F, in a straight line or he can go one of the long routes, such as ;

A,

B, D, C, B, C, E, D, E, F.

lines

between

certain stations,

of the

tions

perplexing

complete route.

little

1

It will

and

Many

problem, though

04.

The

Skipf>er

be noted that he has optional

his selections of these lead to varia

its

readers will find

it

a very

conditions are so simple.

and

the Sea-Serpent.

Mr. Simon Softleigh had spent most of his life between Tooting Bee and Fenchurch Street. His knowledge of the sea was there fore very limited. So, as he was taking a holiday on the south he this was a splendid opportunity for picking up a coast, thought little useful information. He therefore proceeded to " draw " the natives.

"

I suppose," said Mr. Softleigh one morning to a jovial, weatherbeaten skipper, "you have seen many wonderful sights on the rolling

"

seas ?

"

" Bless you,

sir,, yes,"

said the skipper.

118

PY aps

you ve never

MISCELLANEOUS PUZZLES seen a vanilla iceberg, or a mermaid a-hanging out her things to dry on the equatorial line, or the blue-winged shark what flies through the air in pursuit of his prey, or the sea-sarpint " Have you really seen a sea-serpent ? I thought it was uncer

whether they existed." Uncertin You wouldn

tain 44

!

t

say

there was anything uncertin

about a sea-sarpint if once you d seen

The

one. I

seed was

first

as

when

I

was skipper of the Saucy Sally. We

was a-coming round Cape Horn with

a

of

cargo

from the

shrimps

Pacific Islands

when

I

looks over

the port side and sees

a

tremenjus like a

monster

snake, with

ead

its

water

out of

the

and

eyes flash

its

So I shouts to the bo sun to a-bearing down on our ship. the the boat, while I runs below and fetches my sword

ing

fire,

let

down

same what

I

used

eat our cabin-boy sea-sarpint.

when and

I

killed

we

King Chokee, the cannibal

chief as

pulls straight into the track of that there

Well, to make a long story short, when we come along I just let drive at him with that sword o mine, and

side o the beast

*

before you could say Tom Bowling I cut him into three pieces, all of exactually the same length, and afterwards we hauled em aboard

Saucy Sally. What did I do with em ? Well, I sold em to Rio Janeiro, and what do you suppose he done with em ? He used em to make tyres for his motor-car takes a lot to puncture

the

a

feller in

a sea-sarpint

s

skin."

119

THE CANTERBURY PUZZLES "

What was

"

the length of the creature

asked Simon.

?

"Well, each piece was equal in length to three-quarters the There s length of a piece added to three-quarters of a cable. How many a little puzzle for you to work out, young gentleman. " cables long must that there sea-sarpint ave been ? Now, it is not at all to the discredit of Mr. Simon Softleigh that he never succeeded puzzle, for

who

it

may

in

working out the correct answer

to that

little

confidently be said that out of a thousand readers

attempt the solution not one will get

105.

The Dorcas

it

exactly right.

Society.

At the close of four and a half months hard work, the ladies of a certain Dorcas Society were so delighted with the completion of a beautiful silk patchwork quilt for the dear curate that everybody kissed

everybody

himself,

escort

who

else,

young man he had called for, to

except, of course, the bashful

only kissed his

sisters,

whom

There were just a gross of osculations altogether. longer would the ladies have taken over their needle

home.

How

much

work

task

if

the

tennis instead of

sisters

of the curate referred to

attending the

meetings

120

?

Of

had played lawn course we must

MISCELLANEOUS PUZZLES assume that the

ladies attended regularly,

worked equally

all

well.

106.

A mutual

and

am

I

The Adventurous

Snail.

A simple version of the puzzle of the climbing We

everybody.

were

all

taught

it

sure that they

counts as two osculations.

kiss

in

snail

is

apparently intended to inculcate the simple moral that never slip if we can help

it.

This

is

familiar to

the nursery, and

we

it

was

should

the

A

popular story. snail crawls up a pole 12 feet high,

3

ascending

feet

every day and slipping back

2

every night.

How

long does

Of

it

take to

the

to

get

course,

feet

top ? are

we

expected to say the is twelve

answer days,

because the

creature makes an actual advance of

foot

in

1

every

twenty-four hours. this

way.

He

But the modern

infant in

day the snail is summit of its ambition on the tenth day, when it had got to the top. Let

us,

arms

is

not taken in in

enough, that at the end of the ninth 3 feet from the top, and therefore reaches the

says, correctly

however, consider the original

two philosophers were walking

in their

for

it

would cease

to slip

Once upon a time when one of them garden story.

espied a highly respectable member of the Helix Aspersa family, a pioneer in mountaineering, in the act of making the perilous ascent of a wall 20 feet high. Judging by the trail, the gentleman calcu121

THE CANTERBURY PUZZLES lated that the snail ascended 3 feet each day, sleeping

back 2

feet

"

Pray

tell

me," said the philosopher

the same line of business, to the top of the wall

"

how

to his friend,

long will

and descend the other

side.

into

his

daily climbing

is

as

he did

in

his

top of the

gets there

slipping at night as before."

the

version of the puzzle,

true

perhaps be interested

Of

down

in

he same exertion climbing up, and

instantly begin to descend, putting precisely the

sleeping and

who was

The

will

This

slipping

take Sir Snail to climb

it

you know, has a sharp edge, so that when he

wall, as

and

every night.

in

and

my

readers will

working out the exact number

of

days.

always supposed to be equally divided into twelve hours daytime and twelve hours night. course, in a puzzle of this kind the

107.

The

day

is

The Four Princes.

dominions of a certain Eastern monarch formed a perfectly

It happened that the king one day square tract of country. discovered that his four sons were not only plotting against each other, but were in secret rebellion

against

After

himself.

consulting

with his advisers he decided not to exile the princes, but to confine

the four corners of

to

them

the country,

where each should be given a trian gular territory of equal area, beyond the boundaries of which they would

Now, pass at the cost of their lives. the royal surveyor found himself con fronted

owing

by great natural

to the wild character of the country.

The

difficulties,

result

was

that

while each was given exactly the same area, the four triangular dis tricts

were

all

of different shapes,

somewhat

in the

manner shown

in

The

puzzle is to give the three measurements for each of the four districts in the smallest possible numbers all whole the illustration.

furlongs.

In other words,

it

is

required to find (in the smallest

possible numbers) four rational right-angled triangles of equal area.

122

MISCELLANEOUS PUZZLES Plato and the Nines.

108.

Both

and

in ancient

in

modern times the number nine has been

We

considered to possess peculiarly mystic qualities. know, for instance, that there were nine Muses, nine rivers of Hades, and that

Vulcan was nine days

been

falling

down from Heaven.

Then

it

has

confidently

held that nine

make

tailors

man know are

that

nine

days

ders,

and

cat has

and

there

planets,

nine

nine

we

while

;

a

won that

a

nine lives

sometimes

tails.

Most people are

with acquainted some of the curious properties

number

of

the

nine

in

ordinary arith For exam metic. ple, write down a number

containing as

many

figures as

add these figures together, and deduct the sum from the

Now,

the

sum

of the figures in this

new number

will

you like, number.

first

always be a

multiple of nine.

Athens who was not only a He was deeply convinced of the magic properties of the number nine, and was perpetually strolling out to the groves of Academia to bother poor old Plato with " his nonsensical ideas about what he called his lucky number." But the seer one day When of him. rid of a devised Plato way getting his favourite topic, on him a to on inflict lengthy disquisition proposed " Look here, old the philosopher cut him short with the remark,

There was once a worthy man

at

cranky arithmetician, but also a mystic.

123

THE CANTERBURY PUZZLES "

chappie

(that

the nearest translation of the original Greek term bring me the solution of this little

is

"

of familiarity),

when you can

mystery of the three nines I shall be happy to listen to your treatise, and, in fact, record it on my phonograph for the benefit of posterity."

Plato then showed, in the manner depicted in our

illustration,

number by putting them into the form of a fraction. The puzzle he then propounded was, to so arrange the three nines that they will represent the number twenty.

that three nines

may be arranged

so as to represent the

eleven,

that, after working hard at the he one at nine o clock on the morning of day, problem the ninth day of the ninth month, fell down nine steps, knocked out It will be remembered nine teeth, and expired in nine minutes. It

recorded of the old crank

is

for nine years,

that nine

was

his lucky

number.

above

It

was evidently

also Plato

s.

most elementary arithmetical signs are necessary. Though the answer is absurdly simple when you see it, many readers will have no little difficulty in In

the

solving

discovering

little

Take your

it.

only the

puzzle,

and see

pencil

if

you can arrange the

three nines to represent twenty.

109.

Every

mark

knows how to play and each of the two

child

of nine cells, his

Noughts and

You make

game.

a square

players, playing alternately, puts

(a nought or a cross, as the case

may

be) in a

Whichever player

object of getting three in a line. in a line

this

Crosses.

wins with the exulting cry "

cell

first

with the

gets three

:

Tit, tat, toe,

My

last

go

;

Three

jolly

All

a row."

in

butcher boys

a very ancient game. But if the two players have a perfect of it one three of (1) The knowledge things must always happen. first player should win or (3), the first should lose (2) player It is

;

;

the

game should always be drawn. 124

Which is

correct ?

MISCELLANEOUS PUZZLES 1

1

0.

Ovid s Game.

"

Having examined Noughts and Crosses," we will now consider of the game that is distinctly mentioned in the works of " It is in fact the parent of Ovid. Nine Men s Morris," referred to

an extension

sc.

Midsummer Night s Dream" (Act

II.,

Each player

2).

has

"A

in

by Shakespeare three

counters,

which they play alter nately on to the nine

shown

points

in

the

diagram, with the ob ject of getting three in

a

line

and so winning.

But after the counters

are

six

played

they then proceed to move (always to an adjacent

unoccupied

point) with the object.

same

In the above

example White played first and Black has It is now White s move, and he will 7. from 8 to 9, and then, whatever Black may undoubtedly play That is the simple do, he will continue with 5 to 6 and so win.

just \

played on point

game.

Now,

if

both players are equally perfect at the game what

should happen ? Should the first player always win ? Or should the second player win ? Or should every game be a draw ? One

Which

only of these things should always occur.

1

1

1 .

is it ?

The Farmer s Oxen.

A

A

child may propose a problem that a sage cannot answer. " farmer propounded the following question That ten-acre meadow of mine will feed twelve bullocks for sixteen weeks, or eighteen bullocks for eight weeks. How many bullocks could I feed on a :

125

THE CANTERBURY PUZZLES forty-acre field for six weeks, the grass growing regularly "

time

It will

be seen that the

of the grass

is

case

the

sting lies in the

tail.

That steady growth

such a reasonable point to be considered, and yet to

some readers it will cause considerable perplexity. course, assumed to be of equal length and uniform it

all

?

when

appears,

the cattle begin to eat. if

The

The

grass

is,

of

thickness in every

difficulty is

not so great as

you properly attack the question, 112.

The Great Grangemoor Mystery.

Mr. Stanton Mowbray was a very wealthy man, a reputed millionaire, residing in that beautiful old

mansion that has figured so

He was a bachelor, English history, Grangemoor Park. spent most of the year at home, and lived quietly enough. According to the evidence given, on the day preceding the night

much

in

of the

crime he received by the second post a single letter, the him a shock. At ten o clock

contents of which evidently gave at night

he dismissed the

servants, saying that

126

he had some important

MISCELLANEOUS PUZZLES and would be sitting up late. He It was supposed that after all had no attendance. would require some had admitted he bed to person to the house, for one gone of the servants was positive that she had heard loud conversation at business matters to look into,

a very

late hour.

Next morning, floor,

at

a quarter to seven o clock, one of the man Mowbray lying on the

on entering the room, found Mr. shot through the head, and quite dead.

servants,

curious circumstance of the case.

It

was

Now we

come to the

clear that after the bullet

had passed out of the dead man s head it had struck the tall clock in the room, right in the very centre of the face, and actually welded together the three hands, for the clock had a seconds hand that revolved round the same dial as the hour and minute hands.

But

although the three hands had become welded together exactly as

127

THE CANTERBURY PUZZLES they stood in relation to each other at the moment of impact, yet they were free to revolve round the swivel in one piece, and

had been stupidly spun round several times by the servants before Mr. Wiley Slyman was called upon the spot. But they would not

move

separately.

Now, arrest in

inquiries

London

as having

by the police

of a stranger

been seen

in

the neighbourhood led to the

who was

identified by several persons day before the murder, but it what time on the fateful morning he

in the district the

was ascertained beyond doubt at went away by train. If the crime took place after his departure, his For this and other reasons it was of innocence was established. the

first

importance to

the exact time of the pistol shot, the

fix

which nobody in the house had heard. The clock-face in the illustration shows exactly how the hands were found. Mr. sound

of

Slyman was asked and experience, and said

"

to give the police the benefit

directly

of his

sagacity

he was shown the clock he smiled and

:

matter is supremely simple. You will notice that the three hands appear to be at equal distances from one another. The hour hand, for example, is exactly twenty minutes removed from the minute hand that is, the third of the circumference of the dial.

You

The

attach a lot of importance to the fact that the servants have

been revolving the welded hands, but their act is of no consequence whatever, for although they were welded instantaneously, as they are free

on the swivel, they would swing round of themselves into equili Give me a few moments and I can tell you beyond any

brium.

pistol was fired." Mr. Wiley Slyman took from his pocket a notebook, and began to In a few minutes he handed the police inspector a figure it out. slip of paper, on which he had written the precise moment of the crime. The stranger was proved to be an old enemy of Mr. Mowbray s, was convicted on other evidence that was dis covered, but before he paid the penalty for his wicked act he admitted that Mr. Slyman s statement of the time was perfectly

doubt the exact time that the

correct.

Can you

also give the exact time ?

128

MISCELLANEOUS PUZZLES Cutting a

113.

Wood

Block.

An

economical carpenter had a block of wood measuring eight inches long, by four inches wide, by three and three-quarter inches deep.

How

many

by one inch and a of

?

it

pieces,

half,

each measuring two and a half inches,

by one inch and a quarter, could he cut out how you cut them out. Most people

a question of

It is all

would have more waste material

many

pieces could

1

you get out

14.

left

over than

is

necessary.

How

of the block ?

The Tramps and

the Biscuits.

Four merry tramps bought, borrowed, found, or in some other manner obtained possession of a box of biscuits, which they agreed to divide equally

amongst themselves

at breakfast

next morning.

In

the night, while the others were fast asleep under the greenwood tree, one man approached the box, devoured exactly a quarter of the

number

of biscuits, except the

odd one

129

left

over,

which he threw

K

THE CANTERBURY PUZZLES as a bribe to their dog.

and

hit

Later in the night a second man awoke of what remained and

on the same idea, taking a quarter

odd biscuit to the dog. The third and fourth men did same in turn, taking a quarter of what they found and the precisely

giving the

odd biscuit to the dog. In the morning they divided what remained equally amongst them, and again gave the odd biscuit to the animal. Every man noticed the reduction in the

giving the

contents of the box, but, believing himself to be alone responsible,

made no comments. biscuits

acquired

that it

there

What

is

the

smallest

possible

could have been in the box

?

130

number

when

they

of first

SOLUTIONS THE CANTERBURY PUZZLES The Reve

1.

s

Puzzle.

The 8 cheeses can be removed in 33 moves 10 cheeses in 49 moves and 21 cheeses in 321 moves. I will give my general method of solution in the cases of 3, 4 and 5 stools. ;

;

Write out the following

The

first

row

table to

any required length

contains the natural numbers.

The

:

second row

is

found by adding the natural numbers together from the beginning.

The numbers numbers

in

contains

the

in

successive

found by doubling the

row are obtained by adding together the row from the beginning. The fourth row

the third

the second

powers

in turn

of 2, less

1 .

The

each number of that

next

series

series

is

and adding

number that stands above the place where you write the result. This table will at once last row is obtained in the same way.

The

131

K 2

THE CANTERBURY PUZZLES any number of cheeses with three stools, for numbers with four stools, and for pyramidal numbers with In these cases there is always only one method of solu stools.

give solutions for triangular five

that

tion

is,

of piling the cheeses.

In the case of three stools, the

first

and fourth rows

us that

tell

4 cheeses may be removed in 15 moves, 5 in 31,7 in 127. The second and fifth rows show that, with four stools, 10 may be re moved in 49, and 21 in 321 moves. Also, with five stools, we find from the third and sixth rows that 20 cheeses require moves, and 35 cheeses 35 moves. But we also learn from the table the Thus with four stools and cheeses, necessary method of piling. the previous column shows that we must make piles of 6 and 3, which that is we first pile the 6 7 and 7 moves respectively will take 7 moves on one stool then we pile the next 3 smallest cheeses in then remove the largest cheese cheeses on another stool in 7 moves move then replace the 3 in 7 moves and finally replace the in 6 in 7 making in all the necessary 49 moves. Similarly we are 1

1

1

1

1

1

;

1

;

;

1

;

;

1

told that with five stools

which If

35 cheeses must form

will respectively take

the

number of cheeses

1

1

1 ,

49 and

1

piles of 20,

and

1

4,

5 moves.

in the case of four stools

and

not triangular,

is

in the case of five stools

pyramidal, then there will be more than one way of

making the sidiary

This

quired.

with the

But to

I

and sub

piles

tables

will

be re

is

the case

Reve s 8

cheeses.

will leave the

work out

reader

for himself the

extension of the problem. 2.

rh

ph

rh

rh

The Pardoner

s

Puzzle.

The diagram will show how the Pardoner started

from the large black town and visited all the other towns once, and once only, in fifteen straight pilgrimages. 132

SOLUTIONS The Miller

3.

The way

s

Puzzle.

to arrange the sacks of flour

is

as follows

:

2, 78,

1

56,

Here each pair when multiplied by its single neighbour makes the number in the middle, and only five of the sacks need be moved. There are just three other ways in which they might have been 39, 4.

arranged (counting the reversals as require the moving of

more

The Knight

4.

The Knight off

on

declared that as

his shield,

by reference

many

to the ac

companying diagram:

A, B, C, and D, and there are 66 squares of this size to be formed;

Join

they

all

as

Puzzle.

575 squares could be marked

How

this

result

is

(DOOOO @oooooooo ooooooo

o

@

ooo

A, E, F, G, 48 A, H, I, J,

the size gives

s

with a rose at every corner.

may be realised

achieved

different, of course), but

sacks.

ooo o

;

32; B, K,L, M, 19;

B,N,0,P,

10;

B,Q,

R, S, 4 E, T, F, C, 57 I, U, V, P, 33 ;

;

;

H,W,X,J,15; K,Y, Z, M, 3 E, a, b, D, 82 H, d, M, D, 56 ;

;

;

G, 42 K, g, f, C, 32; N, h, z, F, 24; K, h, m, b, 14; K, O, S, D, 16; K, n, p, G, 10 K, q, r, J, 6 Q, t, p, C, 4 Q, u, r, i, 2. The total number is thus 575. These groups have been treated as of them represented a different sized square. This is if each

H,

e,

f,

;

;

correct

B,

K,

;

;

with the one exception that the squares of the form exactly the same size as those of the form

N, O, P, are h,

m,

b.

133

THE CANTERBURY PUZZLES The Wife of Bath

5.

s

Riddles.

The good

lady explained that a bung that is made fast in a barrel another bung that is falling out of a barrel because one of them

is

like

is

in secure

poser

is

and the other

is

readily understood

mand came from

the father

also

insecure.

The

little

relationship

when we

are told that the parental

(who was

also in the

com

room) and not from

the mother.

The Host

6.

The

s

Puzzle. "

puzzle propounded by the jovial host of the

Tabard

"

Inn

Southwark had proved more popular than any other of the " " whole collection. I that I see, my merry masters/ he cried, have sorely twisted thy brains by my little piece of craft. Yet it is of

but a simple matter for me to put a true pint of fine old ale in each of these two measures, albeit one is of five pints and the other of three pints, without using any other measure whatsoever."

The

*

Tabard" Inn thereupon proceeded

host of the

how

to explain

apparently impossible task could be done. He first filled the 5-pint and 3-pint measures, and then, turning the tap, allowed the barrel to run to waste, a proceeding against which the company protested, but the wily man showed that he was aware

to the pilgrims

this

much more than eight pints of do not the solution of the puzzle. affect contents, however, closed the tap and emptied the 3-pint into the barrel

that the cask did not contain

;

ale.

The

He then filled

the

3-pint from the 5-pint emptied the 3-pmt into the barrel transferred the two pints from the 5-pint to the 3-pint filled the 5-pint from the ;

;

;

barrel, leaving

one pint

now

in the barrel

;

filled

3-pint from 5-pint

;

allowed the company to drink the contents of the 3-pint filled the drank 3-pint from the 5-pint, leaving one pint now in the 5-pint ;

;

the contents of the 3-pint barrel into the 3-pint. of ale in

crowd

;

He

each measure,

to

and finally drew off one pint from the had thus obtained the required one pint the great astonishment of the admiring

of pilgrims.

134

SOLUTIONS 7.

Clerk of Oxenford

s

Puzzle.

The illustration shows how the square is to be cut into four pieces and how these pieces are to be put together again to make a magic

square.

It will

long diagonals

be found that the four columns, four rows and two

now add up 8.

The

to

34

in

every case.

The Tapisers Puzzle.

had to be cut along the lines into three together and form a perfect square, with the pat

piece of tapestry

pieces so as to

fit

tern properly matched.

It

was

also stipulated in effect that

one

of

i g

$

3

3

5

the three pieces must be as small as possible. The illustration shows how to make the cuts and how to put the pieces together, while one of the pieces contains only twelve of the

135

little

squares.

THE CANTERBURY PUZZLES 9.

The Carpenter

Puzzle.

s

The carpenter said that he made a box whose internal dimensions were exactly the same as the original block of wood, that is, 3 feet foot by foot. He then placed the carved pillar in this box by and filled up all the vacant space with a fine, dry sand, which he carefully shook down until he could get no more into the box. Then he removed the pillar, taking great care not to lose any of the sand, 1

1

which, on being shaken down alone in the box, filled a space equal one cubic foot. This was, therefore, the quantity of wood that

to

had been

cut away. 10.

The Squire

Puzzle

of Yeoman.

s

the

The illustration will show how three of the arrows were removed each

to a

neighbour

ing square on the signboard of " the Chequers" Inn, so that still

no arrow was

The

another.

in line

with

black dots indi

which the

cate the squares on

three arrows originally stood. 11.

As there the letters

Puzzle.

are eighteen cards bearing

"CANTERBURY

GRIMS," write in a circle, as

Then

Nuns

The

the numbers

shown

write the

first

in the letter

PIL to

1

18

diagram.

C

against

and each successive letter against the second number that happens to be This has been done as far vacant. 1,

as the second

R.

If

the reader

Y

pletes the process by placing and so on, he will get the

com against 2,

letters

136

all

P

against 6,

placed

in

I

against

the

1

0,

following

SOLUTIONS order

CYASNPTREIRMBLUIRG,

:

arrangement

for the cards,

C

which

is

at the top of the

being

the

required

pack and

G

at the bottom.

The Merchant

12.

Puzzle.

s

This puzzle amounts to finding the smallest possible number that and the number itself as has exactly sixty-four divisors, counting 1

divisors.

therefore,

The

have ridden

four and four, last

number

least

in single

and so

manner being

in

file,

might,

pilgrims

two and two, three and

three,

on, in exactly sixty-four different ways, the

a single

The Merchant was

row

possible along an ordinary road

The

of 7,560.

were going over certainly would not be

to say that they

careful

a common, and not to mention

13.

The

7,560.

is

its size,

for

it

!

Man

of Law

s

Puzzle.

The

fewest possible moves for getting the prisoners into their dungeons in the required numerical order are twenty-six. The

men move

in the following

order

1 ,

:

2, 3,

1 ,

2, 6, 5, 3,

1,

2, 6, 5,

As there is never more 1,2, 4, 8, 7, 1, 2, 4, 8, 7, 4, 5, 6. than one vacant dungeon to be moved into, there can be no ambiguity in the notation. 3,

14.

The Weavers Puzzle.

The illustration shows clearly how the Weaver cut his square of beautiful cloth into four pieces of exactly the

same

size

and

shape, so that each piece con tained an embroidered lion and castle

unmutilated in any way.

1

There were

5.

The Coo^s Puzzle.

four portions of

venison pasty to be distributed

warden

among 137

pie

and four portions

of

eight out of eleven guests.

THE CANTERBURY PUZZLES But

five

pasty,

out of eleven will only eat the pie, four will only eat the

and two are

to

willing

eat

combination must

fall

the warden pie

distributed entirely

is

into

one

of

Any

either.

of the following groups,

among

the five

possible

(i.)

first

Where

mentioned,

(ii.) where only one of the accommodating pair is given pie, (iii.) where the other of the pair is given pie, (iv.) where both of the The numbers of combinations are (i.) = 75, (ii.) pair are given pie. = 50, (iii.) = 0, (iv.) = 0, making in all 45 ways of selecting the 1

1

1

A

eight participants.

many people

great

will give the

answer

as

by overlooking the fact that in forty cases in class (iii.) precisely the same eight guests would be sharing the meal as in class (ii.), though the accommodating pair would be eating differently of the two dishes. This is the point that upset the calculations of the 185,

company. 16.

The number

that the

The Sompnour

Sompnour

s

Puzzle.

confided to the

Wife

of

Bath was

twenty-nine, and she was told to begin her count at the Doctor of

who

who who

in the illustration standing the second on count of twenty-nine falls on the Shipman, The second count falls on the Doctor, steps out of the ring. The remaining three counts fall respectively on next steps out.

the

Cook,

Physic,

her

right.

will

The

be seen first

the Sompnour, have been left therefore,

and the in

The

Miller.

possession had

it

ladies would,

not been for the

Any multiple of 2,520 added have served the same purpose, beginning the

unfortunate error of the good Wife.

29 would

to

also

count at the Doctor.

1

7.

The Shipman

s

Puzzle.

two hundred and sixty-four different ways in which ship Magdalen might have made her ten annual voyages without ever going over the same course twice in a year. Every

There are

just

the

year she must necessarily end her tenth voyage at the island from which she first set out.

138

SOLUTIONS \B.

The Monk s Puzzle.

The Monk might have placed dogs in the kennels in two thousand nine hundred and twenty-six different ways, so that there should be ten dogs on every

from twenty

to

forty,

and

side.

as

The number of dogs might vary Monk kept his animals

long as the

within these limits the thing was always possible.

19.

The Puzzle of the

Prioress.

The Abbot of Chertsey was quite correct. shaped cross may be cut into four pieces that will

form

a

perfect

square.

How

this

is

done

is

The fit

curiously-

together and

shown

in

the

illustration.

20.

The Puzzle of the Doctor of Physic.

Here we have indeed

a knotty problem. Our text-books tell us spheres are similar, and that similar solids are as the cubes of corresponding lengths. Therefore, as the circumferences of the two

that

all

were one foot and two feet respectively and the cubes of one and two added together make nine, what we have to find is two These other numbers whose cubes added together make nine. numbers clearly must be fractional. Now, this little question has really engaged the attention of learned men for two hundred and phials

fifty

years, but although Peter

century

de F ermat showed

how an answer may be

in the

seventeenth

found in two fractions with a

denominator of no fewer than twenty-one 139

figures, not

only are

all

THE CANTERBURY PUZZLES the published answers, by his method, that I have seen inaccurate, but nobody has ever published the much smaller result that I now

T1 Lhe cubes L or

.

print.

make

41528(15644:97 34sf 7i6826~6o

J 6 7 fi70.2~4 6 7 503. JJ J i.L and IUFGTIGS^GO added together j.

exactly nine, and, therefore, these fractions of a foot are the

measurements

the

of

circumferences

the two phials that the

of

Doctor required to contain the same quantity of produced. An eminent actuary has taken the trouble

numbers and If

finds

my

cube out these

result quite correct.

the phials were one foot and three feet

respectively, then

liquid as those

to

in

circumference,

an answer would be that the cubes

and iff its 2 s added together make exactly 28. See

"The

of iff 46 111

also

No. 61,

Silver Cubes."

21.

The Ploughman

s

Puzzle.

The illustration shows how the sixteen trees might have been planted so as to form as many as

fifteen

rows

straight

with four trees in every row. This is in excess of

what was

for a long

time believed to be the

maximum rows

number

with our present ledge I cannot ously fifteen

"

beaten,

I

number

of

have a strong pious opinion rows obtainable. 22.

The Franklin

s

of

possible, and though

know rigor

demonstrate

rows cannot

that

be

"

that

it

is

the

highest

Puzzle.

The answer to this puzzle is shown in the illustration, where the numbers on the sixteen bottles all add up to 30 in the ten 140

SOLUTIONS The

straight directions. consists in

trick

the fact that,

al

though the six bottles (3, 5, 6, 9, 10 and 15) in which the flowers have been placed are not removed, yet the six

teen need not occupy exactly

the same position on the table as before.

to the

23.

square

is

in

left.

The Squire

The

HE.&

The

formed one step further

fact

portrait

in a single line

s

Puzzle.

may be drawn

because

it

con

which an odd number of lines meet, but it is absolutely necessary to begin at one of these points and end at One point is near the outer -extremity of the King s left the other. eye the other is below it on the left cheek.

two

tains only

points at

;

24.

The four

five

bags,

hundred in

The Friar

silver

Puzzle.

s

pennies might have been placed in the

accordance with

the

stated

conditions,

in

exactly

there had been a thousand coins there

894,348 would be 7,049, 2 ways. It is a difficult problem in the partition I have a single formula for the solution of any number of numbers. of coins in the case of four bags, but it was extremely hard to con different ways. 1

struct,

If

1

and the best method

is

to find the twelve separate formulas

for the different congruences to the

25.

A very

little

modulus

The Parson

s

1

2.

Puzzle.

examination of the original drawing will have shown first read the conditions, the

the reader that, as he will have at

puzzle

is

quite impossible of solution.

141

We

have therefore

to look

THE CANTERBURY PUZZLES for some loophole in the actual conditions as they were worded. If the Parson could get round the source of the river, he could then

cross

every

bridge once and

once only on

way as

to

his

church,

shown

annexed

the

in

illustra

That

tion.

was

not

this

pro

we shall soon find. Though the hibited

plan

showed

all

the

bridges

in

his parish,

showed of*

it

"

only part

the

parish

not

It is

itself.

stated

the

that

river did not take its

it

leads to the only possible solution,

answer would

be, therefore, as

we

shown.

must assume that

in

the

and

since

rise

parish, it

did.

The we

should be noted that

It

are clearly prevented from considering the possibility of getting round the mouth of the river because we are told it "joined the sea some

hundred miles miles

to the south/* while

26.

The be cut

E

The Haberdasher s Puzzle.

illustration will

into

square.

A

no parish ever extended a hundred

!

to

Bisect

F

show how the

four pieces that will

A

making

describe the arc

A

fit

triangular piece of cloth

B in D and B C in E produce the E F equal to E B bisect A F in G H F produce E B to H, and E H is ;

;

;

142

may

together and form a perfect line

and the

SOLUTIONS length of the side of the required square H, describe the arc J, and make J

H

E

;

from

K

E

with distance

BE;

equal to

now, from the points D and drop perpendiculars on E J at L and M. If you have done this accurately you will now have the required

K

directions for the cuts. I exhibited this problem before the Royal Society, at Burlington House, on 17th May, 1905, and also at the Royal Institution in the

following month, in the

form

general

"

:

more

A

^.-

New

Problem on Superposition

:

a demonstration that an equi lateral

triangle

can be

cut

into four pieces that may be reassembled to form a square,

some examples method for

with

general

rectilinear

all

forming

a

of

trans tri

angles into squares by dis It was also issued as a challenge to the readers of the Daily Mail (see issues of 1st and 8th February, 1905), but though many hundreds of attempts were sent in there was not a single

section.**

solver.

The Dyers Puzzle.

27.

The

correct answer

formula for

is

18,816 different ways.

six fleurs-de-lys for all

The

squares greater than 2

general

2

is

simply Six times the square of the number of combinations of n things, taken three at a time, where n represents the number of fleurs-de-lys Of course where n is even the remainders in the side of the square. this

in

:

rows and columns

will

28.

will

be even, and where n

is

odd the remainders

be odd.

The Great Dispute between

In this reasoning,

little it

and

the

Sompnour.

we attempted to show how, by sophistical apparently be proved that the diagonal of a square

problem

may

the Friar

143

THE CANTERBURY PUZZLES of the sides. The puzzle was a very obvious fallacy if we admit that the shortest distance between two points is a straight line. But

same length

of precisely the

is

where does the

error

come

two

as

to discover the fallacy, because

it is

in ?

Well, perfectly true that so long as our zig-zag path is " " formed of steps parallel to the sides of the square that path must is

it

be

of the

have

same length

two

as the

sides.

It

does not matter

most powerful microscope obtainable

to use the

if

you

the rule

is

But always true if the path is made up of steps in that way. the error lies in the assumption that such a zig-zag path can ever

become a the

You may

straight line.

that

of steps infinitely

number

is,

of steps that

there

can be

is

go on increasing the number no limit whatever theoretically to

made

but you can never reach a " "

by such a method. In fact it is just as much a jump to a straight line if you have a billion steps as it is at the very outset It would be just as false to pass from the two sides to the diagonal. straight line

we

to say

might go on dropping marbles into a basket

became sovereigns as to say we can steps until they become a straight line.

until

they

number of our the whole thing in

increase the

There

is

a nutshell. 29.

The

Chaucer s Puzzle.

surface of water, or other liquid,

the greater any sphere

is

the less

is

its

is

always spherical

convexity.

;

and

Hence, the top

diameter of any vessel at the summit of a mountain will form the base of the segment of a greater sphere than it would at the bottom.

This sphere, being greater, must (from what has been already said) less convex or, in other words, the spherical surface of the water must be less above the brim of the vessel and consequently

be

;

;

it

will

reader

hold is

elsewhere

less at

therefore free to select any mountain he likes in Italy

The or

!

30.

The number for

the top of a mountain than at the bottom.

The Puzzle of of different

such arrangements,

ways

when

the is

Canon

63,504.

number 144

the

s

Yeoman.

The

general formula

of letters in the sentence

SOLUTIONS is

2n +

(4(2-

-

1,

and

it

is

is

The Manciples Puzzle.

simple Ploughman,

perfectly correct

who was

it

should

so ridiculed for his opinion,

the Miller should receive seven pieces of

:

and the Weaver only one. bread

diagonal readings,

.

31.

The

a palindrome without

2

I)]

As

all

was

money

three ate equal shares of the

be evident that each ate f

of

the eight loaves.

^

and ate f, he contributed Therefore, as the Miller provided ate f, 5 to the Manciple s meal, whereas the Weaver provided and contributed only J. Therefore, since they contributed to the ,

Manciple pieces of

in"

the proportion of 7 to

money

in

1,

the same proportion.

145

they must divide the eight

PUZZLING TIMES AT SOLVAMHALL CASTLE SIR

The many

friends

Of

would

I

of Sir

Hugh de

HIS

Fortibus

PROBLEMS were

so perplexed over

of his strange puzzles that at a gathering of his

retainers

"

HUGH EXPLAINS

he undertook

kinsmen and

to explain his posers.

a truth," said he,

"

some

of the riddles that

I

have put forth

greatly tax the wit of the unlettered knave to rede

try to

show the manner

thereof in such

way

that

all

;

yet will

may have

For many there be who cannot of themselves do all understanding. these things, but will yet study them to their gain when they be given the answers, and will take pleasure therein/* 146

SOLUTIONS The Game of Bandy-Ball.

32.

Hugh

Sir

holes

m

explained,

answer

to this puzzle, that as the nine

were 300, 250, 200, 325, 275, 350, 225, 375, and 400 yards

man

a

if

apart,

could always strike the ball in a perfectly straight line

25 yards or 00 yards, he This is clearly might go round the whole course in 26 strokes. correct, for if we call the 125 stroke the "drive" and the 100 stroke and send

at will a distance of either

it

1

1

"

The first hole could be approach/ he could play as follows reached in 3 approaches, the second in 2 drives, the third in 2 drive, the fifth in 3 approaches, the fourth in 2 approaches and the

:

1

backward approach, the sixth in 2 drives and approach, drive and the seventh in approach, the eighth in 3 drives, and There are thus 26 strokes in all, the ninth hole in 4 approaches. and

drives

1

1

1

1

and the

cannot be performed in fewer.

feat

33.

"

Tilting at the Ring. "

By my halidame had been put then would

varlets

serve,

they

length of

having

which

Sir

Hugh,

some of yon do truly de

"if

for their sins they

know,

well

the

that

mayhap,

exclaimed

!

in chains,

any chain

like rings

is

equal to the inner

width

of

a

ring

multiplied by the

the iron whereof

number

of rings

it is

made.

the rings used in the

tilting

It

and added

to twice the thickness of

may be shown

that the inner width of

was one inch and two-thirds thereof, and the number of rings Stephen Malet did win was three, and those that fell to Henry de Gournay would be nine." = 6 in., The knight was quite correct, for If in. x 3 + in. and If in. x 9 + 1 in. = 16 in. Thus De Gournay beat Malet 1

by

six rings.

The drawing showing

in verifying the

answer and help him 147

the rings to see

may

why

assist

the reader

the inner width of

L 2

THE CANTERBURY PUZZLES a link multiplied by the number of links and added to twice the thick ness of the iron gives the exact length. It will be noticed that every link put on the chain loses a length equal to twice the thickness of the iron.

The Noble Demoiselle.

34.

"Some may

*

here have asked me,

find the cell in the

"how

continued Sir Hugh,

they

Death s Head wherein the noble maiden was cast. Beshrew me but tis easy withal when you do but of the

dungeon

!

know how

to

do

In attempting to it. every door once, and

through

pass

never more, you must take heed that every cell hath two doors or four, which be even numbers, except two

which have but

cells,

certes,

you cannot go

Now,

three.

and out

in

of

the doors

any place, passing through once and no more, if the number all

of

doors be an odd number. But as there

be but two such odd ending

cells,

yet

may we, by

beginning at the one and

make our journey in many ways with success. mark that only one of these odd cells lieth on

at the other, so

I pray you, albeit, to the outside of the dungeon, so we must perforce start therefrom. Marry, then, my masters, the noble demoiselle must needs have been

wasting in the other." "

The drawing odd

will

make

cells" are indicated

that will solve the puzzle certain that

one

you must

this quite clear to

by the is

stars,

the reader.

and one

of the

shown by the dotted

start at

many

line.

It is

routes

perfectly

the lower star and end at the upper

therefore, the cell with the star situated over the

;

The two

left

eye must

be the one sought. 35.

" It

The Archery Butt.

hath been said that the proof of a pudding

thereof,

and by the teeth

of Saint

George

148

I

is

ever in the eating

know no

better

way

of

SOLUTIONS how

showing doing of

may be done

placing of the figures

this

Therefore have

it.

I

in

than by the

suchwise written the numbers that

they do add up to twenty and three in upon the butt.

all

the twelve lines of three

*

that are I

think

it

De Fortibus with my own. The nineteen numbers may be so arranged

well here to supplement the solution of

a few remarks of

add up to any number we may choose to select from 22 to 38 inclusive, except In some cases there are ing 30. that the lines will

several different solutions, but in

the case of 23 there are only two. I

give one of these, and leave the

reader to discover the other for In every instance there

himself.

must be an even number central place,

ber

from 2

18

to

solution has

Every

Thus,

mentary.

number

in

in the

and any such num

the

if

may

occur.

comple

its

for

every

accompanying

drawing we substitute the differ ence between it and 20 we get the solution in the case of 37. Similarly,

from the arrangement

in the original

drawing,

we may

at

once obtain a solution

for the

case of 38.

36.

The Donjon Keep Window.

Hugh had greatly perplexed his chief builder by he should make a window measuring one foot on every

In this case Sir that

demanding side and divided by bars into eight lights, having all The illustration will show how this was to be done. that

if

each side of the window measures one

eight triangular lights "

Of

is

six inches

on every

a truth, master builder,"

149

said

foot,

their sides equal. It will

be seen

then each of the

side.

De

Fortibus slyly to

the

THE CANTERBURY PUZZLES

" is

did not

I

architect,

most certain

it

tell

thee that the

window must be

square, as

it

never could be."

The Crescent and

37.

"

the Cross.

By the toes of St. Moden," exclaimed " when this puzzle was brought up, my poor

Sir

Hugh de

Fortibus

wit hath never shaped

It a more cunning artifice or any more bewitching to look upon. came to me as in a vision and ofttimes have I marvelled at the thing,

seeing

exceed

its

My

ing difficulty.

masters and

men,

it

kins

done

is

in

this wise."

The worthy knight then pointed out that the cres cent

was of a par and some

ticular

what irregular form, the

two

the* cuts be

and c to d being straight lines, and He showed that if being precisely similar. as in figure 1, the four pieces will fit together

distances a to b

the arcs a c and b

made

d

and form a perfect square regard the three curved

as

shown

lines.

in

figure 2,

By now making 150

if

we

there only

the straight cuts

SOLUTIONS also

shown

in figure 2,

we

get the ten pieces that

fit

together, as

and form a perfectly symmetrical Greek cross. The proportions of the crescent and the cross in the original illustration were correct, and the solution can be demonstrated to be absolutely exact and not merely approximate. in figure 3,

I

have a solution

difficult to is

in considerably

fewer pieces, but

it is

far

more

understand than the above method, in which the problem

by introducing the intermediate square.

simplified

The Amulet.

38.

A

at the top of die The puzzle was to place your pencil on the amulet and count in how many diffe .r ways you could trace out " " Abracadabra downwards, always passing from a letter the word ;

to

an adjoining one.

A B

B

R R R

A A A A c

c

c

c

c

A A A A A A D D D D D D D

A A A A A A A A

BBBBBBBBB RRRRRRRRRR A A A A A A A A A A A "

ye, fine fellows," said Sir Hugh to some who had " that at the very first start there be two him to besought explain. B whichever ye select there will be two sevc ways open whichever R ye select of proceeding (twice times two are four) and so there be two ways of going on (twice times four are eight) downwards may so Each letter in order from on until the end. be reached in 2. 4, 8, 16, 32, etc., ways. Therefore, as there be to the bottom, all ye need do is to ten lines or steps in all from

Now, mark :

;

;

A

A

multiply ten 2

s

together and truly the result,

thou dost seek." 151

1

.024,

is

the answer

THE CANTERBURY PUZZLES The Snail on

39.

there

Though

was no need

to take

undoubtedly necessary to find It

given.

Hugh de

its

down and measure the staff,

it is

height before the answer can be

was well known among the friends and retainers of Sir was exactly six feet in height. It will be

Fortibus that he

seen in the original picture that Sir length of

the Flagstaff.

shadow.

his

Therefore,

Hugh s height is just twice the we all know that the flagstaff

the same place and time of day, be also just twice as long as shadow. The shadow of the staff is the same length as Sir

will, at its

Hugh s

height

:

therefore, this

must be twelve

staff

shadow

feet high.

is

Now,

six feet

the

long and the flag

by climbing up three feet in the daytime and slipping back two feet by night, really snail,

in a day of twenty-four hours. At the end of nine days it is three feet from the top, so that it reaches its journey s end on the tenth day. " The reader will doubtless here exclaim, This is all very well,

advances one foot

but

how were we to know the height " how tall he was No, it was

stated

but

!

was none the

it

less clearly indicated to

window

Sir

which

stated to be one foot square

Hugh

his height will

?

not stated in so the reader

In the original illustration to the

in these matters.

is

Hugh

of Sir

is

shown standing

It

who

inside.

sharp

window

in

Therefore, as

be found by measurement to be just six times the window, he evidently stands just six feet in

side height of the

boots

is

Donjon Keep

against a wall, the

on the

was never

many words,

in

his

!

40.

Lady

Isabel

s

Casket.

The last puzzle was undoubtedly a hard nut, but perhaps difficulty does not make a good puzzle any the less interesting when we are shown the

The accompanying

diagram indicates exactly de Fitzarnulph s casket was inlaid with square pieces of rare wood (no two squares alike) and the strip of This is the only possible gold 10 inches by a quarter of an inch.

how

solution.

the top of

Lady

Isabel

and it is a singular fact (though method of working) that the number,

cannot here show the

solution,

I

subtle

sizes

152

and order

of those

SOLUTIONS squares can be calculated direct from the given dimensions of the strip of gold, and the casket can have no other dimensions than 20 inches square.

The number

in

a square indicates the length in

20

a 10 x i

20 inches of the side of that square, so the accuracy of the answer can

be checked almost

at a glance.

made some general concluding remarks on the occasion that are not altogether uninteresting to-day. " " Friends and retainers," he said, if the strange offspring of my Sir

Hugh de

Fortibus

we have held pleasant counsel to-night hath had some small interest for ye, let these matters serve to call mayhap to mind the lesson that our fleeting life is rounded and beset with Whence we came and whither we go be riddles, and al enigmas. poor wit about which

beit such as these

we may

never bring within our understanding, yet 153

THE CANTERBURY PUZZLES there be will

many

we and they that do come after us Whether success do attend or do not that we make the attempt, for tis truly

others with which

ever strive for the answer.

attend our labour

it

is

well

good and honourable to train the mind, and the wit and the fancy of man, for out of such doth issue all manner of good in ways unfore seen for them that do come after us."

154

THE MERRY MONKS OF RIDDLEWELL The Riddle of

41.

Number

the

the illustration from

baskets in

fish

direction that Brother Jonathan 1 ,

proceed as follows, where

basket No. 1

the

and

more

way

this

to 7,

It is

transfer

9

to

revolution to

last

proceed

4

1

to 4, 5 to 8,

8

to

1

1

1

it

to

"

to 12 in the

Starting from

4 means take the fish from basket No. 4 to 2, and complete 0, 6, 7 to to

:

1

1

1

making three revolutions in

,

1

seen to be going.

is 1

2, 3 to

the Fishpond.

all.

Or

you can

:

1,

12 to

3,

2

to 5,

6

to 9,

10 to

1.

easy to solve in four revolutions, but the solutions in three are

difficult to discover.

The Riddle of the Pilgrims.

42. If it

were not

for the

Abbot s

conditions that the

number

of guests

any room may not exceed three, and that every room must be occupied, it would have been possible to accommodate either 24, 27,

in

30, 33, 36, 39, or

42

pilgrims.

so that there shall be twice as

on the lower it

will

floor,

But

many

to

accommodate 24

pilgrims,

sleeping on the upper floor as

and eleven persons on each side of the building, to leave some of the rooms empty. If, on

be found necessary

the other hand,

we

try to put

up 33, 36, 39 or 42

pilgrims,

we

shall

we

are obliged to place more than three Thus we know that the number of persons in some of the rooms. find that, in every case,

announced (whom, it will be remembered, it was accommodate under the conditions of the Abbot) must

pilgrims originally possible to

155

THE CANTERBURY PUZZLES have been 27, and three

since

that,

more than this number were ac

3

2

!!

3 lllllM

provided

with

beds,

the

number pilgrims was

of

total

:;

JLlM 8 Rooms

tually

Mil

8 Rooms OH Lower

on Upper Floor

Floor

30.

The accompany 1

1

1

ing diagram

how

shows

might be arranged, and if in each instance they

we regard

2

3

2

1

1

j

B-u 8Roorns on Upper Floor

8 Rooms on Lower

Floor.

the

upper floor

as

placed above the lower one, it will

be seen that there are eleven persons on each side as many above as below.

of the building

and twice

The Riddle of the Tiled Hearth.

43.

The

correct answer

is

shown

in the illustration.

line (either horizontally, vertically, or diagonally)

the same design, and only three plain If,

after

lions

tiles

are used.

the

placing

you

fall

four

into the error

of placing four other tiles of

another pattern, instead of only three, you will be

left

with four places that must be occupied by plain tiles.

The placing

secret

four

and only three the others.

in

consists of

one of

kind

each

of

No

tile

with another

is

tile

in

of

SOLUTIONS The Riddle of the Sack Wine.

44.

The

question

was

Did Brother Benjamin take more wine from

the bottle than water from the jug ? Or did he take more water from the jug than wine from the bottle ? He did neither. The

same quantity

wine was transferred from the

of

bottle as

water was

taken from the jug. Let us assume that the glass would hold a There was a pint of wine in the bottle and a quarter of a pint. pint of water in the jug.

After the

manipulation the bottle

first

and the jug one

contains three-quarters of a pint of wine,

water mixed with a quarter of a pint of wine.

away a

transaction consists in taking that

is

fifth

Now,

pint of

the second

of the contents of the jug,

water mixed with one-fifth of a quarter thus leave behind in the jug four-fifths of a

one-fifth of a pint of

We

of a pint of wine.

quarter of a pint of wine, that

from the jug

to the bottle

is

we

transfer

(one-fifth of

a pint)

one- fifth of a pint, while

an equal quantity

of water.

45.

There were

1

00

The Riddle of the

pints of

wine

Cellarer.

in the cask,

and on

John the Cellarer had stolen a pint and replaced water.

99

After the

first

theft the

wine

left

in

it

thirty occasions

with a pint of

the cask would be

pints ; after the second theft the wine in the cask would be 1 pints (the square of 99 divided by 100) ; after the third theft

lift

there would remain 1

00)

of

;

?$$? (the cube of 99 divided by the square of would remain the fourth power

after the fourth theft there

99 divided by

the cube of 100; and after the thirtieth theft, power of 99 divided by

there would remain in the cask the thirtieth

the twenty-ninth power of 100. This by the ordinary method of calculation gives us a number composed of 59 figures to be divided But by the use of logarithms by a number composed of 58 figures !

it

may be

quickly ascertained that the required quantity

9

73i oV pints of wine nearly 26*03 pints.

left in

The

is very nearly Consequently the cellarer stole monks doubtless omitted the answer for

the cask.

the reason that they had no tables of logarithms, and did not care to

157

THE CANTERBURY PUZZLES face the task of making that long and tedious calculation in order to " to a nicety,* as the wily cellarer had stipulated. get the quantity

By

a simplified process of calculation,

I

have ascertained that the

exact quantity of wine stolen would be

26*029962661 7 95772699849076832850577473237376473235 1

1

55652999 pints.

A

man who would

involve the monastery in a fraction of

fifty-eight decimals deserved severe punishment.

46.

The

The Riddle of the Crusaders.

answer

correct

is

there would

that

have been 602,176

who

could form themselves into a square 776 by 776, and after the stranger joined their ranks, they could form 1 3 squares Crusaders,

1

of

5,329 men

that

47.

The

is,

73 by 73.

The Riddle of St. Edmondsbury. %

aware

that there are prime numbers and composite 1,111,111 cannot be a prime number, because if it were the only possible answers would be those proposed by Brother Benjamin and rejected by Father Peter. Also it cannot have

reader

is

whole numbers.

more than two

Now,

factors or the

answer would be indeterminate.

239

x

As

4649

fact, 1,111,111 equals (both primes), and since each cat killed more mice than there were cats, the answer must be 239 cats. See also the Introduction.

a matter of

48.

The

The Riddle of the Frogs Ring.

fewest possible moves in which this puzzle can be solved The black figures on I will give the complete solution.

are 118.

white discs move in the directions of the hands of a clock, and the white figures on black discs the other way. numbers in the order in which they move. make a simple move or a leaping move

158

The

following are the

Whether you have will

to

be clear from the

SOLUTIONS position, as

you never can have an be played

in brackets are to

9, 10, 6, 5, 4, 3, 2, 7, 8, 9, 10,

12, (7, 8, 9, 10, 9, 10,

1

1,

have made

1

1,

1

1

1

over

8 moves within the

:

enclosed

6, 7, 8, 6, 5, 4, 7, 8,

(6, 5, 4, 3, 2, 1), 6, 5, 4, 3, 2,

1

12), 7, 8, 9, 10,

6, 5, 4, 3, 2, 8, 9, 10,

The moves

alternative.

five times

1,

1

1

1,

1,

6, 5, 4, 3, 2, 12, 7, 8,

4, 3, 2, 10,

1

1,

2.

We thus

conditions, the black frogs

changed places with the white ones, and in the positions stipulated.

159

1

and

1

have

2 are side by side

THE STRANGE ESCAPE OF THE KING S JESTER "

Thereafter Although the king s jester promised that he would make the manner thereof plain to all," there is no record of his I will therefore submit to the reader having ever done so. views as to the probable solutions to the mysteries involved.

49.

When

my own

The Mysterious Rope.

"

divided his rope in half/ it does not follow each half the original length of the rope. No doubt he simply untwisted the strands and so divided it into two He ropes, each of the original length but one half the thickness. that

the jester

he cut

it

into

two

parts,

to tie the two together and make a rope nearly twice the original length, with which it is quite conceivable that he made good his escape from the dungeon.

would thus be able

50.

The Underground Maze.

How his

way

did the jester find

maze in had simply

out of the

He

the dark

?

to

his

grope

way

to a wall

and then keep on walking without once removing his left

from

from A, the dotted to the

left.

If

line will

the reader

make

tries

hand the

(or

right

wall.

the route clear

hand)

Starting

when he

goes

the route to the right in the same

160

SOLUTIONS way he

will

be equally successful

;

in fact, the

two routes

unite

and

cover every part of the walls of the maze except those two detached one piece like a U, and the other like a parts on the left-hand side This rule will apply to the majority of mazes and distorted E. puzzle gardens, but if the centre were enclosed by an isolated wall in the form of a split ring the jester would simply have gone round and >

round

this ring.

The Secret Lock.

51.

This puzzle entailed the finding of an English word of three each letter being found on a different dial. Now, there

letters,

no English word composed of consonants alone, and the only No English word vowel appearing anywhere on the dials is Y. and has the two other letters consonants, and all the begins with is

Y

words

of three letters

S

with an

or have

four consonants

do not

little

doubt that

in

or

word

middle, and the only

can be

Y (with two consonants) either begin R as their second letter. But these Therefore Y must occur in the appear.

ending

H, L,

this

that

I

can find

was the word.

"

is

PYX,"

At any

and there

rate,

it

solves

our puzzle.

Crossing the Moat.

52.

No a

man

the

end

doubt some of a boat on

in

tiller

rope

!

But

my

readers will smile at the statement that

smooth water can it

is

a

fact.

If

pull

himself

across with

the jester had fastened the

rope to the stern of the boat and then, while standing bows, had given a series of violent jerks, the boat would have been propelled forward. This has often been put to a practical test, of his

in the

and

it

is

said that a speed of

attained.

(See

W. W. 53.

Rouse

two or three

miles an hour

" Ball

s

may be

Mathematical Recreations.")

The Royal Gardens.

This puzzle must have struck many readers as being absolutely " The jester said I had, of a truth, entered every one

impossible.

:

161

M

THE CANTERBURY PUZZLES of the sixteen gardens once,

shown

route

the

follow

that there

no

is

difficulty in

B

and never more than once." the

accompanying diagram

once entering

all

If

we

we find

the gardens but one

garden containing the exit B. The difficulty to get into the garden with a star, because if we leave the garden we are compelled to enter it a second time before escaping,

before reaching the is

in

last

B

and no garden may be entered twice. The trick consists in the fact that you I

may

enter that starred garden without

necessarily

when

-

the

leaving

other.

If,

the jester got to the gateway

where the dotted

makes a sharp had been to hide in the starred garden but after he had put one foot through the door line

bend, his intention

!

;

J_

way, upon the star, he discovered it was a false alarm and withdrew, he

l

I

A I

" truly

say

I

:

entered

the

put my foot and part of my body in it, and did not enter the other garden twice, because, after once going in

starred garden because I

could

never

left it until I

and

possible,

which the

54.

The

I

made my

exit at

was doubtless

it

B."

This

is

the only answer

that

jester intended.

Bridging the Ditch.

solution to this puzzle

explained by the

illustration.

best

is

If

he

had placed his eight planks, in the manner shown, across the angle of the ditch he would have been able to cross without

king

s jester

safely

away

much

The

trouble.

might thus have well overcome as

he has

told us that

all

his difficulties

he succeeded

162

in doing.

and got

THE SQUIRE S CHRISTMAS PUZZLE

PARTY HOW The

THE VARIOUS TRICKS WERE DONE

record of one of Squire Davidge

made by

annual

Puzzle Parties,"

young lady relative, who had often Stoke Courcy Hall, does not contain the

the old gentleman

spent a merry Christmas at

" s

s

So I will give my own answers to make them as clear as possible to those who

solutions of the mysteries.

the puzzles and try to

may be more

or less novices in such matters.

55. It is

From

The Eleven Pennies.

rather evident that the trick in this puzzle

was

as follows

:

then add four (to those already taken away) and you leave nine in the second heap of those the eleven coins take five

removed

;

!

56.

The Three Tea-cups.

Miss Charity Lockyer clearly wanted to "get level" with the of the last puzzle, for she had a trick up her sleeve quite as good as his own. She

propounder

proposed that ten lumps of sugar should be placed in three tea-cups, so that

there should be an

number

of

every cup. figures

lumps

The

odd in

illustration

shows Miss Charity

on the cups indicate the number 163

of

s

answer, and the

lumps that have been M 2

THE CANTERBURY PUZZLES separately

them.

placed in

By

placing the cup that holds one

one that holds two lumps, it can be correctly stated lump that every cup contains an odd number of lumps. One cup holds seven lumps, another holds one lump, while the third cup holds inside the

three lumps.

It is

evident that

if

a cup contains another cup

it

also

contains the contents of that second cup.

The Christmas

57.

Geese.

Farmer Rouse sent exactly 101 geese to market. Jabez first sold Mr. Jasper Tyler half of the flock and half a goose over (that is 50i + i, or 51 geese, leaving 50) he then sold Farmer Avent a third of what remained and a third of a goose over (that is 6f + i, ;

1

he then sold

Widow

Foster a quarter of what remained and three-quarters of a goose over (that is 8i + i or 9 geese, leaving 24) ; he next sold Ned Collier a fifth of what " " he had left and gave him a fifth of a goose for the missus (that is or

4t

1

7 geese, leaving 33)

+

i,

;

or 5 geese, leaving 19).

He

then took these 19 back to his

master.

58.

This puzzle,

little jest

on the part

and the face

the figure

9 on

The Chalked Numbers. of

Major Trenchard is another trick boy on the extreme right, with

of the roguish

his back,

showed

clearly that

he was

in the secret,

I have no doubt (bearing in mind whatever that secret might be. to the s hint as numbers the Major being "properly regarded")

that his

answer was that depicted in the 164

illustration,

where boy No.

SOLUTIONS 9

stands on his

the total

head and

number into 6. This makes and by making boys 3 and 4 278 and 5346, the figures get

so converts his

an even number

36

change places with 7 and 8, we each case, add up to

of which, in

1

8.

1

There are just three other 2 457, 1467 3 68

which the boys may be grouped 458. 2358, and 236

ways

in

71

59.

My only

diagram

way

will

Tasting the

show how

this

Plum Puddings. puzzle

twenty-one

end

is

within the conditions laid down.

with holly at the top left-hand corner, in

1

:

we

to

be solved.

strike out all the

straight strokes, taste the steaming hot

of the tenth stroke,

60.

and end

Under

Everybody was found

to

at the

the

puddings

pudding

second sprig of

the Mistletoe

at the

holly.

Bough.

have kissed everybody

else

the mistletoe, with the following additions and exceptions

165

It is

Starting at the pudding

once under :

No

male

THE CANTERBURY PUZZLES kissed a male

wife

;

twice kiss

all

the

;

woman

no man kissed a married

;

the bachelors and boys kissed

widower did not

each other.

kiss

Every

except his the maidens and

all

own girls

anybody, and the widows did not was returned, and the double perform kiss

In making a list of the company, we kiss. can leave out the widower altogether, because he took no part in

ance was to count as one the osculatory exercise.

7 Married couples 3 Widows

14 3

12 Bachelors and Boys 10 Maidens and Girls

.

.

.

.

.....

if

once, the

everyone of these 39 persons kissed everybody else of kisses would be 741, and if the 12 bachelors

number

and boys each kissed the 10 maidens and add 120, making a total of 861 kisses. kissed a married

42

kisses

kisses

;

;

and

number

But

own

other than his

once again, we must as no married man

wife,

we

must deduct 1

as

have, therefore, to deduct

from the above the

woman

girls

no male kissed another male, we must deduct 7 no widow kissed another widow, we must deduct 3

as

We

kisses.

10

39 Persons

Total

Now,

12

total of

861, and the

of kisses that

were

42+171+3 = 216

result,

1

kisses

645, represents exactly

actually given

under the mistletoe

bough. 61.

The

Silver Cubes.

There is no limit to the number of different dimensions that will give two cubes whose sum shall be exactly seventeen cubic inches.

Here

is

the answer in the smallest possible numbers.

One

of the

cubes must measure 2tif if inches along each edge, and the other must measure JMSf inch. If the reader likes to undertake

silver

the task of cubing each

by

itself)

he

number

will find that

(that

is,

when added

equal seventeen cubic inches.

See

the Doctor of Physic."

166

multiply each

number twice

together the contents exactly

also

No. 20,

"The

Puzzle of

THE ADVENTURES OF THE PUZZLE CLUB The Ambiguous Photograph.

62.

One by

one the members the

of the

Club succeeded

in discovering

the

Ambiguous Photograph, except mystery key Herbert Churton, who was at length persuaded to "give it up. Baynes then pointed out to him that the coat that Lord Marksford

the

to

of

*

was carrying over his arm was a lady s coat, because the buttons are on the left side, whereas a man s coat always has the buttons on the right-hand side.

Lord Marksford would not be

likely to

walk

with a lady s coat over his arm unless he about was accompanying the owner. He was therefore walking with the the streets of Paris

lady.

As they were talking "Here you are," he Don t from Dovey

a waiter brought a telegram to Baynes. " wire reading the message.

A

said, after

bother about photo.

:

Find lady was the

That settles it. You s sister, passing through Paris. might notice that the lady was lightly clad, and therefore the coat But it is clear that the rain was only a might well be hers.

gentleman

sudden shower, and no doubt they were close to their destination, and she did not think it worth while to put the coat on."

63. Melville

simple

s

The Cornish Cliff Mystery. Cliff Mystery was very Yet it was an ingenious trick that the two would have completely succeeded had not

explanation of the Cornish

when he gave

criminals adopted,

it.

and

it

167

THE CANTERBURY PUZZLES our friends from the Puzzle Club accidentally appeared on the scene. This is what happened When Lamson and Marsh reached the :

Marsh

stile,

alone walked to the top of the

larger boots in his hands.

Arrived

changed the boots and walked backwards

own

cliff,

Lamson s

with

the edge of the

at

to the

stile,

cliff,

he

carrying his

boots.

This

manoeuvre accounts

little

for the smaller footprints

showing

a deeper impression at the heel, and the larger prints a deeper impression at the toe, for a man will walk more heavily on his heels

when

going forward, but will

toes in walking backwards.

make a deeper impression with the It will

also account for the fact that

the large footprints were sometimes impressed over the smaller ones, but never the reverse also for the circumstance that the larger foot ;

prints

showed a

a smaller stride

stride, for a man will necessarily take when walking backwards. The pocket-book was

shorter

intentionally dropped, to lead the police to discover the footprints,

and so be

set

on the wrong

64.

scent.

The Runaway Motor-Car.

Russell found that there are just twelve five-figure numbers that

have the peculiarity that the three

all

first

two

figures multiplied

by the

the figures being different, and there being no

last

will

produce a number with exactly the same five figures, in a different But only one of these twelve begins with a 1, namely, order. 14926. Now, if we multiply 14 by 926, the result is 12964, which contains the same five figures. The number of the motor car

was therefore

1

4926.

2465 42678, 5 246, 57834, 75231, 78624, 87435, 72936, 65281, 65983 and 86251.

Here

are the other eleven numbers

65.

The

:

The Mystery of Ravensdene Parkin which the Ravensdene Mystery

diagrams show that there are two different ways

routes of the various persons involved in the

may be

1

1 ,

traced, without

any path ever crossing another. 168

It

depends

SOLUTIONS whether the

butler,

gamekeeper

cottage,

s

the north of the

who

E, went to the north

hall.

or

south

the

of

the

and the gamekeeper, A, went to the south or But it will be found that the only persons

could have approached

Mr.

Cyril Hastings without crossing a

It was, path were the butler, E, and the man, C. however, a fact bed five minutes before midnight, whereas

that the butler retired to

Mr. Hastings did not leave

his

friend

house

s

park

midnight. entered the

C.

at

66.

The

until

man who

Therefore, the criminal must have been the

field

The Buried Treasure.

must have contained between

79 and

1

1

80

acres

to

Had the measurements been 3, be more exact, 79*37254 acres. 2, and 4 furlongs respectively from successive corners, then the field 1

would have been 209*70537 acres different

ways

in

area.

of attacking this problem, but

the pleasure of working out his

own

169

I

solution.

There are will leave the

several

reader

THE PROFESSOR S PUZZLES 67.

The Coinage Puzzle.

The on the

point of this puzzle turns fact

that

the magic

if

square were to be composed of whole numbers adding up 15 in all

in

ways, the 2 must be placed one of the corners. Other

wise fractions must be used, and these are supplied in the puzzle

by the employment and half-crowns.

of sixpences

give

I

the

arrangement requiring the fewest possible current English coins It will

fifteen.

one, the

68.

be seen that the amount

sum required

TTze

in the total

The

first

la

of these puzzles

based on a similar prin

ciple,

though

much

easier,

it

is

really

because the

condition that nine of the

stamps must be values

a

makes

simple

each corner

Postage Stamps

Puzzles.

is

in

of different

their selection

matter,

is

a fractional

being a whole number of

though

how

they are to be placed requires a little thought or

170

shillings.

SOLUTIONS one knows the

until

trial

rule respecting putting the

I

the

in

fractions

l-U

corners.

give the solution. I also show the solution

second stamp puzzle. All the columns, rows, and

to the

add up Is. 6d. no stamp on one square and the conditions

diagonals

There

is

did not forbid this omission.

The

stamps at present in

circulation are these

U, 5s.,

HJ.,

2