Logic Puzzles

 

Logic Puzzles Miran Kim Ben Seelbinder Matthew Sgambati

 

What are logic puzzles? •

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“A puzzle deriving rom the mathematics !eld o deduction" Produced b# $harles Lutwidge %odgson A puzzle that can be solved using logical reasoning &t helps wor' with rules o logic (and) or) *or) etc+, Programs that carr# out logical reasoning use these puzzles to illustrate capabilities

 

-he Master o Logic Puzzles •

.igh School dropout who got a Ph+%+ in logic at Princeton

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Wrote onin logic puzzlesman# such boo's as Alice as Alice Puzzle-Land  and  and To Mock a Mockingbird  •

Most amous or his “Knights and Knaves Problem"

/a#mond Smull#an

 

Knights and Knaves & don3t lie4

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5either do &4

0ncounter two people Knights alwa#s tell the truth Knaves alwa#s lie 1igure out whether each person is a 'night or a 'nave rom their statements

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0*ample2 A sa#s) “At least one o us is a 'nave" and B sa#s nothing

 

Knight and Knave Problem A sa#s “At least one o us is a 'nave" and B sa#s nothing+ P(*,2 * is a 'night 6P(*,2 * is a 'nave Suppose A is a 'nave+ 6P(A, 7 What A sa#s must be alse 6P(A, 8 6P(B, 7 1 $hec'2 6P(A, 8 6P(B, 7 - 8 6P(B, 7 -

&mpossible

A is a 'night and what A sa#s must be true+ P(A, 6P(A, 8 6P(B, 6P(B,

∴

Answer2 A is a 'night+ B is a 'nave+

 

Knight and Knave Problem A sa#s “-he two o us are both 'night" and B sa#s “A is a 'nave+" P(*,2 * is a 'night 6P(*,2 * is a 'nave Suppose A is a 'night+ P(A, 7 What A sa#s must be true P(A,9P(B, 7 P(B, 7 -

&mpossibl e

.owever) B sa#s 6P(A, 7 P(A, 7 1 A is a 'nave and what A sa#s is alse+ 6P(A, 7 P(A,9P(B, 7 1 9P(B, 7 1

Answer2 A is a 'nave+ B is a 'night+

i s a 'nave, is true+  B is a 'night because his statement (A is

 

Knight and Knave Problem A sa#s) “& am a 'nave or B is a 'night" and B sa#s nothing+ –

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A is a 'night B is a 'night

Both A and B sa#) “& am a 'night+" –

$annot determine the answer

A sa#s) “We are both 'naves" and B sa#s nothing+ –

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A is a 'nave B is a 'night

A sa#s) “B is a 'night" and B sa#s) “-he two o us are opposite t#pes+" –

A is a 'nave

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B is a 'nave

 

Knight) Knave and Sp# Problem rom Alice rom  Alice in Puzzle-Land  Puzzle-Land  Added rule2 Sp# can lie or tell the truth+ -here is one sp#) one 'night) and one 'nave+ A sa#s that $ is a 'nave+ B sa#s sa#s that A is a 'nig 'night+ ht+ $ sa#s sa#s “& am the sp#+" Which one is the sp#) which one is the 'night) which one on e is the 'nave? Knight(*,2 * is a 'night Knave(*,2 * is a 'nave Sp#(*,2 * is a sp# 1rom $3s statement) state ment) $ can3t be a 'night 'n ight because a 'night never lie about his identit#+ identit#+ -hereore) $ is either a 'nave or a sp#+ sp#+

 

Knight) Knave and Sp# Problem cont+ rom Alice rom  Alice in Puzzle-Land  Puzzle-Land  Suppose $ is a sp#+ 6Knight($, 9 6Knave($, 9 Sp#($, 7 6Kna 6K nave ve($ ($,, 7 - (s (sim impl pli!c i!cat atio ion, n, Knave($, 71 What A sa#s is alse) so A is 'nave+

-here is one sp#) one 'night) and one 'nave+ A sa#s that $ is a 'nave+ B sa#s that A is a 'night+ $ sa#s “& am the sp#+"

 6Knight(A, 9 Knave(A, 9 6 Sp#(A, 7 6Knigh 6Kn ight(A t(A,, 7 - (si (simpl mpli!c i!cati ation, on,

B must be a 'night) and what B sa#s must be true+&mpossible $hec'2 : $ isn3t a sp#+ Knight(A, 7 6Knight(A, 7 1 Answer2 $ is a 'nave+ A is telling the truth) so A is a 'night+ B is a sp#+

 

Multiple $hoice .elp  ;ou  ; ou encounter a problem on an e*am with onl# answer choices) tthe he