Panduan Olimpiade Akm Matematika Nasional Online

 

R CMZ C RJ RJQJU QJU] ] L@DIRD MJ  

tdg td g m c uo uodd kj kji i ip ipu u c i tji tji td tdk k iu md mdsd sdcd cd

 

]DCNKH] QM/QIR/QIH/IHGHQDQ^H/ZIZI

 

@H]HU EJ@HKHCN

L`dipdhmj HKI Ihtjihtdkh Chsdlch` ijruphkhc sjeuhg jvjct klipjtdsd yhcn mdsj`j mdsj `jcn cnnh nhrrhk hkhc hc l` l`jg jg Cd Cdaj aj ey Dc Dcml mlcj cjsd sdh h (j (jvj vjct ct lr lrnh nhcd cdzj zjrr rj rjsi sidd md wd wd`h `hyh yhg g Ehc Eh cyu yuih ihs) s) mh mh`h `hi i rhc hcnk nkh h ij ijc cyh yhie ieut ut Hs Hsjs jsij ijc c Ch Chsd sdlc lch` h` 52 5258 58.. Kjn jndh dhth thc c dc dcdd mdsj`j mds j`jcnn cnnhr hrhk hkhc hc mj mjcn cnhc hc tuo tuouhc uhc ijc ijcnuo nuodd kji jihip hipuhc uhc mhs mhshr hr Iht Ihtji jihtd htdkh kh ht hthu hu cuij cu ijrh rhsd sd hc hchk hk eh ehcn cnsh sh mh mhc c ij ijif ifhs hsd` d`dt dths hsdd nj njcj cjrh rhsd sd uc uctu tuk k ej ejrp rprj rjst sths hsdd mh mh`h `hi i l`dipdhmj tdcnkht Chsdlch` Klipjtds Klipj tdsdd dcd md` md`hk hkshc shchk hkhc hc sja sjahr hrh h mhrdcn mhrdcn (lc (lc`dc `dcj) j) mjcn mjcnhc hc ghr ghrhph hphc c ij ijskd skdpu puc c mdtjcnh mdtj cnhg g sdtuh sdtuhsd sd phcm phcmjida jida njc njcjr jrhsd hsd Dcml Dcmlcjsd cjsdh h tjt tjthp hp ejr ejrsjih sjihcnh cnhtt uct uctuk uk ijr ijrhdg hdg prjsthsd.

 

QTHUH] & KJ]JC]ZHC ZIZI  

  Rjsjrth tjrihsuk kjmh`hi sh`hg shtu khtjnlrd khtjnlrd pjsjrth yhdtu QM-QIR-QIH-IHGHQDQ^H/ZIZI QM-QIR-QIH-IHGHQD Q^H/ZIZI   Ijid`dkd khrtu dmjctdths rjsid (Khrtu pj`hohr/Uhplrt/K]I/ pj`hohr/Uhp lrt/K]I/ K]R/Euktd K]R/Euktd `hdc yhcn ijieuktdkhc ehgwh pjsjrth ejchr ihsuk mh`hi khtjnlrd pjsjrth)

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  Ijcyjmdhkhc GR/@hptlp GR/@hptlp mhc hksjs dctjrcjt uctuk ijcnjrohkhc slh` l`dipdhmj

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  Ijcyj`jshd Ijcyj`jshdkhc khc sjiuh h`ur pjcmhfthr pjcmhfthrhc hc

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  Ij`hkshchkhc l`dipdhmj mjcnhc ouour

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  Rjsjrth yhcn tjreuktd ij`hkukhc tdcmhkhc ijrundkhc pdghk phcdtdh ihupuc pjsjrth `hdc hkhc md mdskuh`dfdkhsd mdskuh`dfdk hsd mhrd pjr`liehhc

 

]DIJ@DCJ RJCMHF]HUHC (8: Hprd`-8 Ijd 5258)

RJCTDQDGHC (5 mhc 1 Ijd 5258)

RJCNZIZIHC FDCH@ (: Ijd 5258)

EHEHK FDCH@

RJCNZIZIHC GHQD@ FDCH@

(4 Ijd 5258)

(81 Ijd 5258)

 

H@ZU RJCMHF]HUHC

Qghrj plstjr mhc fl``lw hkuc dcsthnrhi phcdtdh

Ijcndsd `dck rjndstrhsd pjsjrth l`dipdhmj

Ij`hkukhc pjcmhfhthrhc vdh ^H

Ijcmhphtkhc klmj pjsjrth l`dipdhmj

Ihsuk kj nrup tj`jnrhi pjsjrth sjsuhd ojcohcn mhc thcnnh` pd`dghc pjcydsdghc

Ijcndkutd pj`hkshchhc l`dipdhmj

 

8.

Rjsjrth Rjsj rth ijihg ijihghid hid phcm phcmuhc uhc yhcn hmh md edt.`y/ edt.`y/Rhc Rhcmuhc muhcLHKI LHKII I

5.

Qghrj plstjr mhc ahptdlc ahptdlc jvjct l`diphdmj l`diphdmj kj kj dcsthnrhi dcsthnrhi hthu 1 nrup nrup ^H ^H (`dck plstjr hmh md edt.`y/RlstjrmhcahptdlcLHKII)

1. =.

Fl``lw hku Fl``lw hkuc c dcst dcsthnr hnrhi hi Bcdaj Bcdajeydcm eydcmlcjsdh lcjsdh mhc Bshtu Bshtuprjs prjsthsd. thsd.dm dm Ij`hkukhc Ij`hkukh c pjcmhfthrhc pjcmhfthrhc kj hmidc ^H ^H 27>> 6=77 :442 mjcnhc ijcndrdikhc chih mhc mhc hsh` sjkl`hg, euktd sghrj mhc fl``lw. fl``lw. (Zctuk khtjnlr khtjnlrdd uiui clc ihghsdswh aukup mdtu`ds ZIZI)

:.

Rjsjrth mdilglc ijiehah mjcnhc shkshih eh`hshc pjshc mhrd hmidc khrjch pjshc klcfdr klcfdrihsd ihsd mdeh`hs ltlihtds

6.

Rjsjrth ijid`dg whktu whktu pjcydsdghc l`dipdhmj mjcnhc mjcnhc ahrh ihsuk kj nrup tj`jnrhi yhcn sjsuhd mjcnhc mjcnhc  ojcohcn pjcmdmdkhc mhc thcnnh` thcnnh` pd`dghc pjcydsdghc. (Ehehk pjcydsdghc pjcydsdghc hmh muh lpsd thcnnh` thcnnh` 5/1 Ijd 5258)

>.

Ijcndsd `dck flriu`dr rjndstrhsd yhcn mdejrdkhc phcdtdh mh`hi nrup tj`jnrhi (aukup 8 kh`d)

7.

Rjsjrth ijcmhphtkh ijcmhphtkhc c klmj pjsjrth mhrd phcdtdh phmh thcnnh` 8 Ijd Ijd 5258 (Ihksdih` (Ihksdih` sjej`ui ohi pjcydsdghc mdiu`hd)

 

KJ] KJ]JC] JC]ZHC ZHC RJ RJQJU QJU]H ]H 

  Rjsjrth mdehnd ijcohmd = khtjnlrd yhdtu? - Qdswh QM/ID/Qjmjrhoht (Qlh` yhcn mduodkhc uctuk ojcohcn QM mdiu`hd kj`hs 1) - Qdswh QIR/I]Q/Qjmjrhoht - Qdswh QIH/QIK/Qjmjrhoht

- Ihghsdswh/ZIZI (Nuru ihsuk mh`hi khtjnlrd ZIZI)    Rjsjrth mdcyhthkhc tjrmhfthr sjahrh shg mh`hi l`diphdmj sjtj`hg ijcmhphtkhc klmj pjsjrth mhrd phcdtdh 

  Rjsjrth yhcn yhcn tdmhk ijcyj`jshdkhc ijcyj`jshdkhc sj`urug sj`urug rhcnkhdhc h`ur pjcmhfthrhc pjcmhfthrhc tdmhk mhpht ijcndkutd l`dipdhmj

 

KJ] KJ]JC] JC]ZHC ZHC L@ L@DIR DIRDHM DHMJ J 

  Ojcds L`dipdhmj L`dipdhmj ? L`dipdhmj L`dipdhmj Lc`dcj Lc`dcj Ujsid Ujsid

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  Ijmdh klipjtdsd klipjtdsd yhcn mdnuchkhc ? Nlln`j Flri (]dmhk hmh zlli)

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  Ouhrh yhcn hkhc mdhied` yhdtu ouhrh 8-82 pjr khtjnlrd

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  Rjcmhfthrhc yhcn tj`hg md`hkukhc tdmhk mhpht mdehth`khc, kjauh`d mjcnhc h`hshc kjsjghthc.

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  Qjiuh dcflrihsd hkhc hkhc md ejrdthgukhc ij`h`ud lffdadh` haaluct sladh` ijmdh khid mhc nrup pjsjrth

 

KJ]JC]ZHC EHEHK RJCTDQDGHC  

  Rjcydsdghc Rjcydsdghc sjiuh khtjnlrd khtjnlrd md`hkshchkhc md`hkshchkhc 5 ghrd phmh thcnnh` thcnnh` 5/1 Ijd 5258   Qjtdhp pjsjrt pjsjrth h ejehs ijid`dg ijid`dg thcnnh` thcnnh` pjcydsdghc pjcydsdghc

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  ^hktu pj`hkshchhc uctuk uctuk thcnnh` thcnnh` 5 mhc 1 Ijd ? Khtjnlrd QM ? Ruku` 27.22 ^DE ‑ 24.12 ^DE Khtjnlrd QIR ? Ruku` 82.22 ^DE ‑ 88.12 ^DE Khtjnlrd QIH/QIK ? Ruku` 81.22 ^DE ‑ 8=.12 ^DE Khtjnlrd Ihghsdswh / Ziui ? Ruku` 8:.12 ^DE ‑ 8>.22 ^DE

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  Rjtucou Rjtucouk k tjkcds pj`hkshchhc pj`hkshchhc tjs hkhc mdshiphdkhc mdshiphdkhc ij`h`ud nrup tj`jnrhi tj`jnrhi

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  @dck slh` ehehk pjcydsdghc pjcydsdghc hkhc mdkdrdikhc mdkdrdikhc phmh ghrd pj`hkshchhc pj`hkshchhc mdmh`hi nrup.

 

KJ]JC]ZHC FDCH@ 

  Rjsjr Rjsjrth sklr ≪ 822 th yhcn mhpht ijihsukd ehehk fdch` hmh`hg pjsjrth yhcn ijid`dkd sklr

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  Rjsjrth yhcn ihsuk ehehk fdch` ij`hkukhc pjcmhfthrhc u`hcn fdch`ds mjcnhc ijcndsd ijc ndsd `dck pjcm pjcmhfth hfthrhc rhc fdch` mhc ijcn ijcndrdi drdikhc khc eukt euktdd pji pjiehy ehyhrh hrhc c rjn rjndstr dstrhsd hsd fdch` sjejshr 5:.222 kj clilr phcdtdh. (Ehnd pjsjrth yhcn tdmhk ihsuk fdch` tdmhk pjr`u ij`hkukhc rjndstrhsd u`hcn hthu pjiehyhrhc)

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  Qlh` mh`hi ehehk fdch` l`dipdhmj l`dipdhmj ijid`dkd oui`hg mhc ihtjrd ihtjrd yhcn shih mjcnhc mjcnhc ehehk eheh k pjcydsdghc, pjcydsdghc, hkh hkhc c tjthpd tjthpd hkh hkhc c hmh pjcn pjcnurh urhcnh cnhc c murhsd pjcnjrohh pjcnjrohhc c slh` mhc pjcdcnkhthc tdcnkht kjsu`dthc sjejshr 82%.

 

FHQD@D]HQ RJQJU]H ∟ Qlh` mhc Rjiehghshc L`dipdhmj HKI Ihtjihtdkh ∟ J-sjrtdfdkht Rjsjrth Chsdlch` (R`us Chih uctuk sj`urug pjsjrth) ∟ J-Qjrtdfdkht Rrjsthsd ejrehralmj sjsuhd pjrl`jghc cd`hd ( Ehnd pjsjrth yhcn ihsuk fdch`) ∟ Rjijrdcnkhthc Chsdlch` (Ehnd sj`urug pjsjrth) ∟ Qlh` sjsuhd ojcohcn pjcmdmdkhc (Ehnd sj`urug pjsjrth) ∟ Hksjs pjijshchc ijmh`d glclrhe`j ijctdlc (Ehnd pjsjrth yhcn ihsuk ]LR 822)

 

KJ]JC]ZHC GHMDHG Ghmdhg Zthih yhcn hkhc mdejrdkhc Ihtjihtdkh Ihtjihtdk h Chsdlch` hmh`hg sjehnhdkjphmh ejrdkut?phrh ouhrh uiui 82 ejshr pjr khtjnlrd L`dipdhmj HKI 

  Ijmh`d Ouhrh (Jihs, (Jihs, Rjrhk, Rjrhk, Rjrucnnu)Nrhtds Rjrucnnu)Nrhtds (Ouhrh (Ouhrh 8-82)

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  Qjrtdfdkht Ajthk Ouhrh, Nrhtds (Ouhrh 8-82)

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  Rdhnhi Ouhrh Ajthk, Nrhtds (Ouhrh 8-82) Vluagjr jr rjnds rjndstrhsd trhsd jvjct jvjct Cdaj ey Dcmlcjsdh Dcmlcjsdh sjcd`hd 5:.222 5:.222    Vluag Cltjs ? Rjsjrth yhcn ejrhmh md Ru`hu Ohwh Lcnkls kdrdi 822% mdthcnnucn phcdtdh, sjmhcnkhc uctuk  ouhrh mhrd `uhr ohwh ohwh lcnkls lcnkls kdrdi md suesdmd phcdtdh phcdtdh :2%.

 

KJ]JC]ZHC IH]JUD MHC QLH@    Ihtjrd

yhcn md `liehkhc hmh`hg ihtjrd Hsjsijc Klipjtjcsd Idcdiui (HKI) Cuijrhsd hthu Ihtjihtdkh.

   Alctlg

slh` HKI mhpht md`dght md `hihc rjsid rjsid kjijcmdkeum gttps?//pusijcohr.kjijcmdkeum.nl.dm/hki/ hthu `hihc `hdc yhcn ijiehghs

slh` HKI)    Ihtjrd uctuk pjsjrth khtjnlrd ihghsdswh /uiui hkhc ijcnnuchkhc ihtjrd QIH tjthpd mjcnhc tdcnkht kjsu`dthc slh` `jedg tdcnnd.    Qlh` `jedg ehcyhk ehcyhk ijcnnuchkhc `lndkh `lndkh hthu pjch`hrhc pjch`hrhc mhc hch`dsds.

 

KJ]JC]ZHC IH]JUD MHC QLH@  

  Qlh` ejroui`hg 12 slh` pjr khtjnlrd ehehk pjcydsdghc   Udcadhc mhc ]dpj Qlh` Ehehk Ehehk Rjcydsdghc 8. 5.

Rd`dghc nhc Rd`dghc nhcmh mh (8: Qlh`) Rd`dghc Rd`dg hc nhc nhcmh mh klip` lip`jks jks (> Qlh`)

1. Ijc Ijcolm olmlgk lgkhc hc (7 slh slh`) `)

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  Udcadhc mhc ]dpj ]dpj Qlh` Ehehk Fdch` 8. Rd`dg Rd`dghc hc nhc nhcmh mh (8: Qlh`) 5.

Rd`dghc Rd`dg hc nhc nhcmh mh klip` lip`jks jks (> Qlh`)

1.

Ijcolmlg Ijco lmlgkhc khc (7 slh`)

=. Ds Dsdh dhc c (: Ql Qlh` h`)) :. Zr Zrhdh hdhc c (8 Qlh Qlh`) `)

 

KJ]JC]ZHC RJCD@HDHC EHEHK RJCTDQDGHC

KJ]JC]ZHC RJCD@HDHC EHEHK FDCH@



  Ohwhehc ejchr mh`hi pd`dghc nhcmh nhcmh mdejrd cd`hd :

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  Ohwhehc ejchr mh`hi pd`dghc nhcmh nhcmh mdejrd mdejrd cd`hd 1

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  Ohwhehc ejchr mh`hi pd`dghc nhcmh klip`jks mdejrd cd`hd 5,: pjr ohwhehc ejchr (Qjtdhp slh` nhcmh klip`jks klip`jks ijid`dkd `jedg mhrd 8 ohwhehc ejchr)

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  Ohwhehc ejchr mh`hi pd`dghc nhcmh nhcmh klip`jks klip`jks mdejrd cd`hd 5,: pjr ohwhehc ejchr (Qjtdhp slh` nhcmh klip`jkss ijid`dkd `jedg mhrd 8 ohwhehc ejchr) klip`jk

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  Ohwhehc ejchr mh`hi mh`hi slh` slh` ijcolmlgkhc ijcolmlgkhc mdejrd cd`hd cd`hd 5,: pjr ohwhehc ejchr (Mh`hi sjtdhp slh` ijcolmlgkhc ijcolmlgk hc tjrmhpht `jedg mhrd 8 ohwhehc ejchr)

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  Ohwhehc ejchr mh`hi urhdhc sdcnkht mdejrd cd`hd 6

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  Ohwhehc ejchr mh`hi urhdhc ijid`dkd kjtjctuhc kjtjctuhc cd`hd ihksdih` 82 uctuk ghsd` ohwhehc mhc cd`hd ihksdih` 82 uctuk pjcoj`hshc yhcn ijcmukucn

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  Ohwhehc sh`hg mdejrd cd`hd cl` (2)

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  ]dmhk ijcndsd ijcndsd ohwhehc mdejrd cd`hd cd`hd cl` (2)

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  Ohwhehc ejchr mh`hi mh`hi slh` ijcolmlgkhc mdejrd cd`hd 5,: pjr ohwhehc ejchr (Mh`hi sjtdhp slh` ijcolmlgkhc tjrmhpht tjrmhpht `jedg mhrd 8 ohwhehc o hwhehc ejchr)

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  Ohwhehc sh`hg mdejrd cd`hd cl` (2) (2)

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  ]dmhk ijcndsd ohwhehc ohwhehc mdejrd cd`hd cd`hd cl` (2)

 

KJ]JC]ZHC RJIJCHCN 

  Rjijchcn yhcn yhcn mdhied` hmh`hg ouhrh 8 ‑ 82 pjr khtjnlrd uctuk pjcnghrnhhc ijmh`d jihs, pjrhk mhc pjrucnnu



  Rjsjrth yhcn ihsuk mh`hi ]LR ]LR 822 ijcmhphtkhc pjcnghrnhhc glclrhe`j ijctdlc

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  Rjijchcn ouhrh mdtjctukhc mdtjctukhc ij`h`ud ij`h`ud uruthc oui`hg cd`hd tjrehdk mhrd pjijrdcnkh pjijrdcnkhthc thc Chsdlch`



  Hphed`h tjrmhpht tjrmhpht muh cd`hd yhcn shih, ihkh hkhc mdhied` mdhied` mhrd pjsjrth yhcn yhcn tjrajpht tjrajpht mh`hi ijcyj`jshdkhc ijcyj` jshdkhc slh`



  Hphed`h hmh muh hthu hthu `jedg pjsjrth yhcn ijid`dkd cd`hd mhc whktu whktu pjcnjrohhc yhcn yhcn shih, ihkh pjijchcn mdpd`dg mhrd pjsjrth yhcn ijid`dkd cd`hd tjrtdcnnd mhrd slh` urhdhc.



  Kjputushc mjwhc ourd tdmhk mhpht mdnhcnnu nunht.

 

FUJXZJC]@T HQKJM XZJQ]DLCQ

H ? Khk, Hphkhg `lieh dcd pjcdpuhc< E ? kjohghthc Kjndhthc Kjndht hc yhcn khidQd`hkhc sj`jcnnhrhkhc ejrsdfijmdh ejrsdfht ht rjsid mhc hihc. hyhcn ihc.dkut ]dmhk hmh ucsur pjcdpuhc `hdccyh. ajk ejejrhph `lieh ijiehctu khid mh`hi mhc gh` ijcyjehrkhc dcflrihsd jvjct dcd. H ? Khk kjchph ghrus phkhd euktd dmjctdths < E ? Zctuk ijihstdkhc sjtdhp pjsjrth yhcn ijcmhfthr sjsuhd mjcnhc khtjnlrd pjsjrth yhcn tj`hg mdtjctukhc. (‐Edhr cnnh phmh elglcn yjj?v) H ? Khk, chctd cnjrohdccyh cnjrohdccyh phkhd hph< E ? Ijcnnuchkhc nlln`j flri.

 

FUJXZJC]@T HQKJM XZJQ]DLCQ

H ? Khk, ejrhrtd mhfthr `liehcyh ejrehyhr yh< E ? Rjcmhft Rjcmhfthrhc hrhc `lieh dcd nrhtds uctuk sj`urug pjsjrth mh`hi ehehk pjcydsdghc, sjmhcnkhc uctuk yhcn ihsuk fdch` ehru hkhc hmh rjndstrhsd u`hcn.

H ? Khk yhcn cnnh ihsuk fdch` mhpjt hph < E ? Qjiuh fhsd`dths yhcn sumhg mdsjeutkhc tjrihsuk j sjrtdfdkht, kjauh`d hksjs pjijshchc ijmh`d. H ? Khk, ihtjrd slh` `liehcyh hph < E ? Ihtjrd yhcn mduodkhc ghcyh ihtjihtdkh sjsuhd ojcohcn pjcmdmdkhccyh.

 

FUJXZJC]@T HQKJM XZJQ]DLCQ

H ? Khk, hmhkhg twdeelccyh< E ? Khid tdmhk ijcyjmdhkhc twdeelc uctuk ehehk pjcydsdghc. Euktd sghrj ghcyh uctuk sghrj plstjr mhc ahptdlc jvjct khid. H ? Ehnhdihch ahrh klcfdrihsd u`hcn pjcmhfthrhc < E ? Kdrdikhc Chih mhc Hsh` sjkl`hg, euktd sghrj mhc fl``lw kj kj clilr hmidc ^H 27>>-6=77-:442 H ? Hph ihksum khtjnlrd mh`hi pjcmhfthrhc < E ? Khtjnlrd yhcn mdihksum hmh`hg khtjnlrd pjsjrth, khiu ihsuk md ojcohcn pjcmdmdkhc yhcn hph.

 

FUJXZJC]@T HQKJM XZJQ]DLCQ

H ? Qjrtdfdkhtcyh edsh uctuk pjcmhfthrhc sjkl`hg khk< E ? El`jg mhc edsh md`hipdrkhc uctuk pjcmhfthrhc, chiuc kjieh`d `hnd kjphmh pjrhturhc sjtdhp sjkl`hg hthupuc ucdvjrsdthscyh yh, khrjch sjtdhp sjkl`hg ijid`dkd pjrhturhc yhcn ejejmh-ejmh. H ? Qjrtdfdkhtcyh hmh cd`hdcyh kh< E ? Zctuk sjrtdfdkht hprjsdhsd tdmhk mdahctuikhc cd`hd pjsjrth, chiuc ehnd pjsjrth yhcn ijcndkutd ehehk fdch` hmh sjrtdfdkh sjrtdfdkhtt prjsthsd yhcn mdsjrthd cd`hd mhc ehralmj.

 

Dcsthnrhi Bcdajey Dcsthnrhi Bcdajeydcmlcjsdh dcmlcjsdh Fhajellk Cdaj ey Dcmlcjsdh Hmidc ^ghtshpp 7>>6=77 7>>6=77:44 :44

QLQDH@ IJMDH DCFLUIHQD  \\\\\\

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