\u201cPortrenin kar\u015f\u0131s\u0131nda konu\u015fan adam\u0131 \u2018John\u2019, portredeki adam\u0131 ise \u2018Bay X\u2019 olarak adland\u0131ral\u0131m ve c\u00fcmleyi John\u2019un a\u011fz\u0131ndan bir kez daha s\u00f6yleyelim: \u201cBen tek \u00e7ocu\u011fum ve Bay X\u2019in babas\u0131, benim babam\u0131n o\u011fludur.\u201d<\/p>\n
Problemin \u00e7\u00f6z\u00fcm\u00fcn\u00fc John yap\u0131yorsa \u015f\u00f6yle d\u00fc\u015f\u00fcn\u00fcr: Peki benim babam\u0131n o\u011flu kim? Ba\u015fka karde\u015fim olmad\u0131\u011f\u0131na g\u00f6re bu yaln\u0131zca ben olabilirim! O halde Bay X\u2019in babas\u0131 benim ve Bay X benim o\u011flum.\u201d<\/p>\n
Problemi biz \u00e7\u00f6z\u00fcyorsak \u015f\u00f6yle d\u00fc\u015f\u00fcn\u00fcr\u00fcz: John tek evlatsa ve Bay X\u2019in babas\u0131, John\u2019un babas\u0131n\u0131n o\u011fluysa, o zaman Bay X\u2019in babas\u0131n\u0131n John olmas\u0131 gerekir ve e\u011fer Bay X\u2019in babas\u0131 John ise o zaman Bay X, John\u2019un o\u011fludur.\u201d<\/p>\n
Vos Savant her iki durumda da adam\u0131n kendi portresine de\u011fil, o\u011flunun portresine bakt\u0131\u011f\u0131n\u0131 ayr\u0131nt\u0131l\u0131 bir \u015fekilde a\u00e7\u0131klayarak yanl\u0131\u015f d\u00fc\u015f\u00fcnen y\u00fczlerce okurunu ikna etmeyi ba\u015far\u0131r.<\/p>\n
D\u00fcnyan\u0131n\u00a0 \u201cen zeki kad\u0131n\u0131\u201d olarak ad\u0131n\u0131 Guinnes Rekorlar Kitab\u0131\u2019na yazd\u0131rm\u0131\u015f olan Marilyn vos Savant bir magazin dergisi olan Parade<\/em>\u2019de \u201cMarilyn\u2019e Sorun\u201d isimli k\u00f6\u015fesinde okurlar\u0131n merak ettikleri sorular\u0131 yan\u0131tl\u0131yordu. Gelen sorular\u0131n \u00e7o\u011fu g\u00fcndelik hayatla ilgili yukar\u0131daki mant\u0131k bilmecesi gibi s\u0131radan sorulard\u0131.<\/p>\n Bir g\u00fcn,\u00a0 Vos Savant\u2019\u0131n bir soruya verdi\u011fi yan\u0131t, f\u0131rt\u0131nan\u0131n da \u00f6tesinde, adeta deprem etkisi yarat\u0131r. Binlerce ele\u015ftiri mektubu gelir. Vos Savant, bu kez, sadece okurlar\u0131n\u0131n de\u011fil, hat\u0131r\u0131 say\u0131l\u0131r bir\u00e7ok matematik\u00e7inin de \u015fiddetli tepkisiyle kar\u015f\u0131la\u015f\u0131r.<\/p>\n Bir matematik\u00e7i \u015f\u00f6yle yazar: \u201cProfesyonel bir matematik\u00e7i olarak halk\u0131n matematik bilgisinin eksikli\u011finden \u00e7ok rahats\u0131z\u0131m. L\u00fctfen hatan\u0131z\u0131 itiraf edin ve ileride daha dikkatli olun.\u201d Ba\u015fka bir matematik\u00e7i: \u201cBu \u00fclkede yeterince matematik cahilli\u011fi var ve d\u00fcnyan\u0131n en y\u00fcksek IQ\u2019sunun bunu yayg\u0131nla\u015ft\u0131rmas\u0131na ihtiyac\u0131m\u0131z yok. Utan\u0131n!\u201d\u00a0 Bir di\u011feri: \u201cHatan\u0131z\u0131 kabul ederseniz rezil bir durumun \u00e7\u00f6z\u00fcm\u00fcne yap\u0131c\u0131 bir katk\u0131n\u0131z olur. Fikrinizi de\u011fi\u015ftirmeniz i\u00e7in ka\u00e7 k\u0131zg\u0131n matematik\u00e7i gerekli?\u201d<\/p>\n Bu problem, pop\u00fcler matematik merakl\u0131lar\u0131n\u0131n \u00e7ok iyi bildi\u011fi \u00fcnl\u00fc Monty Hall problemidir. Ge\u00e7mi\u015fi 1950\u2019lere uzan\u0131r, \u00a0Marilyn vos Savant\u2019\u0131n 1990\u2019da Parade<\/em>\u2019deki k\u00f6\u015fesinde yay\u0131mlamas\u0131yla yeniden g\u00fcndeme gelmi\u015ftir. Ali Nesin\u2019in de Matematik ve Oyun <\/em>isimli kitab\u0131nda yer verdi\u011fi bu problemden habersiz merakl\u0131 okurlar\u0131n da olabilece\u011fini d\u00fc\u015f\u00fcnerek, burada bir kez daha ele almay\u0131 ve bunca g\u00fcr\u00fclt\u00fcn\u00fcn sonras\u0131n\u0131 da aktarmay\u0131 istiyoruz.<\/p>\n Monty Hall Problemi<\/strong><\/p>\n Bir yar\u0131\u015fma program\u0131nda oldu\u011funuzu ve \u00fc\u00e7 kap\u0131dan birini se\u00e7me hakk\u0131n\u0131z oldu\u011funu varsayal\u0131m. Kap\u0131lardan birinin ard\u0131nda bir araba, di\u011ferlerinin ard\u0131nda ise ke\u00e7iler var. Yar\u0131\u015fman\u0131n kurallar\u0131 \u015funlar: Siz kap\u0131y\u0131 se\u00e7tikten sonra, kap\u0131 hemen a\u00e7\u0131lmaz. Kap\u0131lar\u0131n ard\u0131nda ne oldu\u011funu bilen sunucu Monty Hall, \u015fimdi geriye kalan iki kap\u0131dan birini a\u00e7mak zorundad\u0131r ve a\u00e7aca\u011f\u0131 kap\u0131n\u0131n ard\u0131nda mutlaka bir ke\u00e7i olacakt\u0131r. E\u011fer geriye kalan iki kap\u0131n\u0131n ard\u0131nda da ke\u00e7i varsa, kap\u0131lardan birini rastgele se\u00e7ecektir. Monty Hall ard\u0131nda ke\u00e7i olan kap\u0131y\u0131 a\u00e7t\u0131ktan sonra, size ilk se\u00e7iminizi de\u011fi\u015ftirip kalan kap\u0131lardan di\u011ferini se\u00e7mek isteyip istemedi\u011finizi soracakt\u0131r. D\u00fc\u015f\u00fcn\u00fcn ki Kap\u0131 1’i se\u00e7tiniz ve sunucu ard\u0131nda ke\u00e7i olan Kap\u0131 3’\u00fc a\u00e7t\u0131. Daha sonra size “Se\u00e7iminizi 2 numaral\u0131 kap\u0131dan yana de\u011fi\u015ftirmek ister misiniz?” diye sordu. Se\u00e7iminizi de\u011fi\u015ftirmek sizin yarar\u0131n\u0131za m\u0131d\u0131r?<\/p>\n Arabay\u0131 bulmak i\u00e7in yar\u0131\u015fan yar\u0131\u015fmac\u0131 kap\u0131lardan birini, diyelim ki 1\u2019inciyi se\u00e7mi\u015f olsun. Sunucu di\u011fer kap\u0131lardan birini, diyelim ki 3’\u00fc a\u00e7ar ve arkas\u0131nda ke\u00e7i vard\u0131r; yar\u0131\u015fmac\u0131ya 1\u2019inci kap\u0131 yerine 2\u2019inciyi se\u00e7ebilece\u011fini s\u00f6yler. Bu durumda yar\u0131\u015fmac\u0131 arabay\u0131 kazanma olas\u0131l\u0131\u011f\u0131n\u0131 art\u0131rmak i\u00e7in se\u00e7imini de\u011fi\u015ftirmeli midir? Yoksa de\u011fi\u015ftirse de de\u011fi\u015ftirmese de fark etmez mi?<\/p>\n Marilyn vos Savant bu soruya y\u00fczlerce matematik\u00e7iyi \u00e7ileden \u00e7\u0131karacak \u201cde\u011fi\u015ftirmelidir\u201d yan\u0131t\u0131n\u0131 verir ve ilk olarak \u015fu \u00e7\u00f6z\u00fcm\u00fc yapar: Yar\u0131\u015fmac\u0131 kap\u0131lardan birini se\u00e7ti\u011finde, se\u00e7ilen kap\u0131n\u0131n ard\u0131nda araba olma olas\u0131l\u0131\u011f\u0131 1\/3’t\u00fcr ve araba 2\/3 olas\u0131l\u0131kla di\u011fer kap\u0131lardan birinin ard\u0131ndad\u0131r. Sunucunun ard\u0131nda ke\u00e7i olan bir kap\u0131y\u0131 a\u00e7mas\u0131, yar\u0131\u015fmac\u0131ya se\u00e7ti\u011fi kap\u0131n\u0131n ard\u0131nda ne oldu\u011fuyla ilgili yeni bir bilgi vermez. O kap\u0131n\u0131n ard\u0131nda araba olma olas\u0131l\u0131\u011f\u0131 h\u00e2l\u00e2 1\/3’t\u00fcr. Sunucunun verdi\u011fi yeni bilgi, a\u00e7\u0131lan kap\u0131n\u0131n ard\u0131nda araba olma olas\u0131l\u0131\u011f\u0131n\u0131n 0\/3 oldu\u011fudur. Dolay\u0131s\u0131yla araba 2\/3 olas\u0131l\u0131kla h\u00e2l\u00e2 a\u00e7\u0131lmayan kap\u0131n\u0131n ard\u0131ndad\u0131r. Kap\u0131 se\u00e7imi de\u011fi\u015ftirilirse arabay\u0131 kazanma olas\u0131l\u0131\u011f\u0131 2\/3’t\u00fcr, bu nedenle yar\u0131\u015fmac\u0131 se\u00e7imini de\u011fi\u015ftirmelidir.<\/p>\n 9 Eyl\u00fcl 1990 tarihli k\u00f6\u015fesinde yay\u0131mlad\u0131\u011f\u0131 bu \u00e7\u00f6z\u00fcm\u00fcn ard\u0131ndan itiraz mektuplar\u0131 ya\u011fmaya ba\u015flar. Kap\u0131 de\u011fi\u015ftirildi\u011finde kazanma olas\u0131l\u0131\u011f\u0131n\u0131n 2\/3 de\u011fil, 1\/2 oldu\u011fu savunulmaktad\u0131r. Marilyn vos Savant, g\u00f6nderenler aras\u0131nda bir\u00e7ok matematik\u00e7inin de bulundu\u011fu bu mektuplar\u0131n baz\u0131lar\u0131n\u0131 2 Aral\u0131k 1990 tarihli k\u00f6\u015fesinde yay\u0131mlar ve tabloyla ikinci bir \u00e7\u00f6z\u00fcm daha yapar: Yine yar\u0131\u015fmac\u0131n\u0131n ilk olarak 1\u2019inci kap\u0131y\u0131 se\u00e7ti\u011fini varsayal\u0131m.<\/p>\n De\u011fi\u015ftirmezse:<\/strong><\/p>\n De\u011fi\u015ftirirse:<\/strong><\/p>\n Vos Savant, bu \u00e7\u00f6z\u00fcm\u00fcn alt\u0131na \u015f\u00f6yle yazar: \u201cTablolar, yar\u0131\u015fmac\u0131n\u0131n se\u00e7imini de\u011fi\u015ftirmedi\u011finde \u00fc\u00e7 sonu\u00e7tan birinde, de\u011fi\u015ftirdi\u011finde ise \u00fc\u00e7 sonu\u00e7tan ikisinde kazanaca\u011f\u0131n\u0131 kan\u0131tl\u0131yor.\u201d<\/p>\n Bu a\u00e7\u0131klama da tepkileri dindirmez. Vos Savant\u2019\u0131n \u00e7\u00f6z\u00fcm\u00fc tamamen do\u011frudur, ama bir\u00e7ok matematik\u00e7i sezginin oyununa gelmi\u015f, do\u011fru \u00e7\u00f6z\u00fcme \u201cdo\u011fru\u201d diyememi\u015ftir. Vos Savant, 17 \u015eubat 1991\u2019de bu konu \u00fczerine yazd\u0131\u011f\u0131 \u00fc\u00e7\u00fcnc\u00fc k\u00f6\u015fe yaz\u0131s\u0131nda \u201cGer\u00e7eklik sezgiyle b\u00f6ylesine \u015fiddetli bir \u00e7at\u0131\u015fmaya girince insanlar sars\u0131ld\u0131.\u201d diye yazar ve kendisine gelen binlerce mektubun y\u00fczde doksan\u0131n\u0131n verdi\u011fi \u00e7\u00f6z\u00fcme kar\u015f\u0131 oldu\u011funu belirtir. G\u00f6nderenin ismini de belirterek gelen mektuplardan al\u0131nt\u0131lar yapar.\u00a0 Bu mektuplar\u0131n baz\u0131lar\u0131nda as\u0131l ke\u00e7inin o oldu\u011fu ve kad\u0131nlar\u0131n matemati\u011fe erkeklerden daha farkl\u0131 bakt\u0131klar\u0131 iddia edilir.<\/p>\n Vos Savant, sab\u0131rla, verdi\u011fi yan\u0131t\u0131n do\u011frulu\u011funu a\u00e7\u0131klamay\u0131 s\u00fcrd\u00fcr\u00fcr, \u00fc\u00e7\u00fcnc\u00fc ve son olarak ba\u015fka bir yol daha dener: \u201cSunucu arkas\u0131nda ke\u00e7i olan kap\u0131y\u0131 a\u00e7t\u0131ktan sonra \u015fovun sahnesine bir UFO\u2019nun indi\u011fini ve k\u00fc\u00e7\u00fck ye\u015fil bir kad\u0131n\u0131n belirdi\u011fini hayal edin. Sizin hangi kap\u0131y\u0131 se\u00e7ti\u011finizi bilmeksizin, bu kad\u0131ndan a\u00e7\u0131lmam\u0131\u015f iki kap\u0131dan birini se\u00e7mesi istenmi\u015f olsun. Arabay\u0131 bulma olas\u0131l\u0131\u011f\u0131 y\u00fczde ellidir. Ancak bunun nedeni, as\u0131l yar\u0131\u015fmac\u0131ya sa\u011flanan avantaj\u0131, yani sunucunun yard\u0131m\u0131n\u0131, bilmiyor olmas\u0131d\u0131r. E\u011fer \u00f6d\u00fcl 2\u2019inci kap\u0131n\u0131n arkas\u0131ndaysa, sunucu 3\u2019\u00fcnc\u00fc kap\u0131y\u0131 a\u00e7ar; e\u011fer \u00f6d\u00fcl 3\u2019\u00fcnc\u00fc kap\u0131n\u0131n arkas\u0131ndaysa 2\u2019inci kap\u0131y\u0131 a\u00e7ar. Dolas\u0131yla karar\u0131n\u0131z\u0131 de\u011fi\u015ftirdi\u011finiz takdirde e\u011fer \u00f6d\u00fcl 2\u2019inci veya 3\u2019\u00fcnc\u00fc kap\u0131n\u0131n arkas\u0131ndaysa kazan\u0131rs\u0131n\u0131z. Her iki durumda da kazan\u0131rs\u0131n\u0131z! Ama e\u011fer karar\u0131n\u0131z\u0131 de\u011fi\u015ftirmezseniz, sadece \u00f6d\u00fcl\u00fcn 1\u2019inci kap\u0131n\u0131n arkas\u0131nda olmas\u0131 durumunda kazan\u0131rs\u0131n\u0131z.\u201d<\/p>\n Bu a\u00e7\u0131klaman\u0131n ard\u0131ndan tepkiler de\u011fi\u015fmeye ba\u015flar, itiraz eden bir\u00e7ok matematik\u00e7i yelkenleri suya indirir, sonucu kabul etmek zorunda kal\u0131r. Bu sonu\u00e7, elbette t\u00fcm matematik\u00e7ileri hi\u00e7bir \u015fekilde ba\u011flamaz. Problemin olas\u0131l\u0131k teorisinde yer alan ko\u015fullu olas\u0131l\u0131k<\/em> kavram\u0131yla olduk\u00e7a basit bir \u00e7\u00f6z\u00fcm\u00fc vard\u0131r ve bu \u00e7\u00f6z\u00fcm Vos Savant\u2019\u0131n soruyu sormas\u0131ndan \u00f6nce de bilinmekteydi. Teslim etmek gerekir ki, Monty Hall problemi olduk\u00e7a kafa kar\u0131\u015ft\u0131r\u0131c\u0131d\u0131r. Ama bu hik\u00e2yede bana en \u00e7arp\u0131c\u0131 gelen olay, 20\u2019inci y\u00fczy\u0131l\u0131n en b\u00fcy\u00fck matematik\u00e7ilerinden Paul Erd\u00f6s\u2019\u00fcn do\u011fru \u00e7\u00f6z\u00fcme itiraz etmesidir.\u00a0 Paul Erd\u00f6s olas\u0131l\u0131k teorisiyle ilgili bir\u00e7ok \u00f6nemli problemi \u00e7\u00f6z\u00fcme kavu\u015fturmu\u015f \u00fcnl\u00fc bir matematik\u00e7idir. Ama Macar matematik\u00e7i Andrew Vazsonyi, Erd\u00f6s\u2019e problemi anlat\u0131p, yan\u0131t\u0131n kap\u0131y\u0131 de\u011fi\u015ftirmek oldu\u011funu s\u00f6yledi\u011finde \u00e7ok \u015fa\u015f\u0131raca\u011f\u0131 \u015fu yan\u0131tla kar\u015f\u0131la\u015fm\u0131\u015ft\u0131r: \u201cHay\u0131r, bu imk\u00e2ns\u0131z. De\u011fi\u015ftirmekle de\u011fi\u015ftirmemek aras\u0131nda hi\u00e7bir fark yok.\u201d\u00a0 Erd\u00f6s, uzun bir s\u00fcre do\u011fru \u00e7\u00f6z\u00fcme \u201cdo\u011fru\u201d diyememi\u015f, hatta Vazsonyi\u2019ye \u201cBana neden de\u011fi\u015ftirmek gerekti\u011fini s\u00f6ylemiyorsun.\u201d diye \u00e7\u0131k\u0131\u015fm\u0131\u015f, ancak problemin bilgisayardaki sim\u00fclasyonunu izledikten sonra yanl\u0131\u015f d\u00fc\u015f\u00fcnd\u00fc\u011f\u00fcn\u00fc kabul etmi\u015ftir.<\/p>\n Basit bir mant\u0131k bilmecesinden tutun da karma\u015f\u0131k matematik problemlerine kadar, \u00f6n\u00fcm\u00fcze koyulan \u00e7\u00f6z\u00fcm\u00fc anlamak, en az problemi \u00e7\u00f6zmek kadar emek ve \u00e7aba gerektiriyor. Zaman zaman bu da yetmiyor, sezgilerimizin oyununa gelerek matematiksel ger\u00e7e\u011fi g\u00f6zden ka\u00e7\u0131rabiliyoruz, hem de bu i\u015fin uzman\u0131 olsak bile. Bu bak\u0131mdan Monty Hall problemi ve Marilyn vos Savant\u2019\u0131n ak\u0131l dolu \u00e7abas\u0131 olduk\u00e7a ilgin\u00e7 ve \u00f6\u011fretici.<\/p>\n Kaynaklar<\/strong><\/p>\n 1) Hoffman P, Yanl\u0131zca Say\u0131lar\u0131 Seven Adam<\/em>, \u00c7ev. K\u00f6m\u00fcrc\u00fc, D, Sistem Yay\u0131nc\u0131l\u0131k, 1999.<\/p>\n 2) Vos Savant, M, Fleischer, L, Beyin Geli\u015ftirme, <\/em>\u00c7ev. \u015een, C, \u0130m Yay\u0131nlar\u0131, 2000.<\/p>\n","protected":false},"excerpt":{"rendered":" Bir adam duvardaki bir tabloya bakarak \u015funlar\u0131 s\u00f6yler: \u201c Ne k\u0131z, ne de erkek karde\u015fim var, ailenin tek \u00e7ocu\u011fuyum, ama resimdeki adam\u0131n babas\u0131, benim babam\u0131n o\u011flu.\u201d Adam\u0131n bakt\u0131\u011f\u0131 portre kime ait? Bu mant\u0131k bilmecesini, yazarlar\u0131 Marilyn vos Savant ve Leonore Fleischer olan Beyin Geli\u015ftirme isimli kitaptan al\u0131nt\u0131lad\u0131m. Marilyn vos Savant bu bilmeceyi Amerika\u2019da yay\u0131mlanan Parade […]<\/p>\n","protected":false},"author":375,"featured_media":23265,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[157,38,514,510],"tags":[],"class_list":["post-23263","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-120-sayi","category-dergi-sayilari","category-matematik-sohbetleri","category-surekli-bolumler"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/posts\/23263","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/users\/375"}],"replies":[{"embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/comments?post=23263"}],"version-history":[{"count":0,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/posts\/23263\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/media\/23265"}],"wp:attachment":[{"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/media?parent=23263"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/categories?post=23263"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/tags?post=23263"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n\n
\n 1\u2019inci Kap\u0131<\/strong><\/td>\n 2\u2019inci Kap\u0131<\/strong><\/td>\n 3\u2019\u00fcnc\u00fc Kap\u0131<\/strong><\/td>\n Sonu\u00e7<\/strong><\/td>\n<\/tr>\n \n Araba<\/td>\n Ke\u00e7i<\/td>\n Ke\u00e7i<\/td>\n Kazan\u0131r<\/td>\n<\/tr>\n \n Ke\u00e7i<\/td>\n Araba<\/td>\n Ke\u00e7i<\/td>\n Kaybeder<\/td>\n<\/tr>\n \n Ke\u00e7i<\/td>\n Ke\u00e7i<\/td>\n Araba<\/td>\n Kaybeder<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n \n\n
\n 1\u2019inci Kap\u0131<\/strong><\/td>\n 2\u2019inci Kap\u0131<\/strong><\/td>\n 3\u2019\u00fcnc\u00fc Kap\u0131<\/strong><\/td>\n Sonu\u00e7<\/strong><\/td>\n<\/tr>\n \n Araba<\/td>\n Ke\u00e7i<\/td>\n Ke\u00e7i<\/td>\n Kaybeder<\/td>\n<\/tr>\n \n Ke\u00e7i<\/td>\n Araba<\/td>\n Ke\u00e7i<\/td>\n Kazan\u0131r<\/td>\n<\/tr>\n \n Ke\u00e7i<\/td>\n Ke\u00e7i<\/td>\n Araba<\/td>\n Kazan\u0131r<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n ![\"\"](\"https:\/\/bilimvegelecek.com.tr\/wp-content\/uploads\/2018\/04\/marilyn-vos-savant-19-226x300.jpg\" "\\"\\"")
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