Matematiksel d\u00fc\u015f\u00fcnmenin zarafetiyle dolu \u00fc\u00e7 g\u00fczel oyunu \u00e7\u00f6z\u00fcmleriyle birlikte payla\u015f\u0131yorum.<\/p>\n
Say\u0131 tahmin oyunu<\/strong><\/p>\n Arkada\u015f\u0131n\u0131z k\u00e2\u011f\u0131da yazd\u0131\u011f\u0131 iki basamakl\u0131 do\u011fal say\u0131y\u0131 tahmin etmenizi istiyor. Her tahmin sonras\u0131nda do\u011fru olan basamak say\u0131s\u0131n\u0131 0, 1 ve 2 rakamlar\u0131ndan biriyle s\u00f6yleyece\u011fini bildiriyor. \u00d6rne\u011fin, k\u00e2\u011f\u0131tta 54 yaz\u0131l\u0131 ve siz 24 dediniz. Arkada\u015f\u0131n\u0131z \u201c1\u201d diyor, sonras\u0131nda 45 dediyseniz bu kez hi\u00e7bir basama\u011f\u0131n yerini do\u011fru bilemedi\u011finiz i\u00e7in \u201c0\u201d yan\u0131t\u0131n\u0131 veriyor. Elbette, \u201c2\u201d dedi\u011finde say\u0131y\u0131 bildi\u011finizi s\u00f6ylemi\u015f oluyor.<\/p>\n En az ka\u00e7 tahminde k\u00e2\u011f\u0131ttaki say\u0131y\u0131 bulmay\u0131 garantilersiniz<\/strong>?<\/p>\n \u00c7\u00f6z\u00fcm<\/strong>. \u00d6nce, 10\u2019dan ba\u015flayarak ve 11 art\u0131rarak \u015fu 9 say\u0131y\u0131 s\u00f6ylemelisiniz: 10, 21, 32, 43, 54, 65, 76, 87, 98. Son s\u00f6yledi\u011finiz say\u0131ya kadar arkada\u015f\u0131n\u0131z susmu\u015f ve 98 dedi\u011finizde \u201c2\u201d demi\u015fse k\u00e2\u011f\u0131ttaki say\u0131 98\u2019dir. E\u011fer \u201c1\u201d dediyse 99. \u015eimdi di\u011fer durumlara bakal\u0131m, aradan bir say\u0131y\u0131 alal\u0131m. \u00d6rne\u011fin 32 say\u0131s\u0131n\u0131 s\u00f6yledi\u011finizde arkada\u015f\u0131n\u0131z \u201c2\u201d dediyse k\u00e2\u011f\u0131ttaki say\u0131 32\u2019dir. E\u011fer \u201c1\u201d dediyse k\u00e2\u011f\u0131ttaki say\u0131 33, 34, 35, 36, 37, 38, 39 veya 42, 52, 62, 72, 82, 92 say\u0131lar\u0131ndan biridir. Bu durumda 4\u2019\u00fcnc\u00fc tahmin olarak \u201c33\u201d derseniz, e\u011fer gelen yan\u0131t \u201c2\u201d ise k\u00e2\u011f\u0131ttaki say\u0131 33\u2019t\u00fcr, arkada\u015f\u0131n\u0131z \u201c1\u201d dediyse k\u00e2\u011f\u0131ttaki say\u0131 34, 35, 36, 37, 38, 39 say\u0131lar\u0131ndan biridir ve bu say\u0131lar\u0131 teker teker s\u00f6yleyerek en fazla 5 tahminde k\u00e2\u011f\u0131ttaki say\u0131y\u0131 bulursunuz. E\u011fer arkada\u015f\u0131n\u0131z \u201c0\u201d dediyse bu kez arad\u0131\u011f\u0131n\u0131z say\u0131 42, 52, 62, 72, 82, 92 say\u0131lar\u0131ndan biridir ve yine en fazla 5 tahminde k\u00e2\u011f\u0131ttaki say\u0131 bulunabilir. B\u00f6ylece ba\u015flang\u0131\u00e7ta 3 tahmin ve ard\u0131ndan 33 diyerek 1 tahmin ve son olarak 5 tahminle toplam 9 tahmin yaparak k\u00e2\u011f\u0131ttaki say\u0131 bulunur.<\/p>\n Ba\u015flang\u0131\u00e7ta s\u00f6ylenen 9 say\u0131dan herhangi birini de yukar\u0131daki gibi incelersek en fazla 9 tahminde k\u00e2\u011f\u0131ttaki say\u0131n\u0131n bulunabilece\u011fi g\u00f6r\u00fcl\u00fcr.<\/p>\n Say\u0131 \u00e7\u0131karma oyunu<\/strong><\/p>\n A <\/em>ve B <\/em>gibi iki oyuncu 1000 say\u0131s\u0131ndan say\u0131lar \u00e7\u0131kararak \u015f\u00f6yle bir oyun bir oyun oynuyorlar: \u00d6nce A<\/em>, bu say\u0131dan herhangi bir asal say\u0131n\u0131n do\u011fal say\u0131 kuvveti (a <\/em>asal, n <\/em>do\u011fal say\u0131 olmak \u00fczere a<\/em>n <\/em>say\u0131lar\u0131) olan istedi\u011fi bir say\u0131y\u0131 \u00e7\u0131kar\u0131yor. Sonras\u0131nda B<\/em>, kalan say\u0131dan yine herhangi bir asal say\u0131n\u0131n do\u011fal say\u0131 kuvveti olan istedi\u011fi bir say\u0131y\u0131 \u00e7\u0131kar\u0131yor. Sonra yine A <\/em>kalan say\u0131 i\u00e7in ayn\u0131 i\u015flemi yap\u0131yor ve oyun s\u0131ras\u0131yla bu \u015fekilde devam ediyor. En son say\u0131y\u0131 \u00e7\u0131karan, yani sonucu 0 bulan oyuncu oyunu kazan\u0131yor.<\/p>\n Bu oyunda hangi oyuncu nas\u0131l oynarsa oyunu kazanmay\u0131 garantileyebilir?<\/p>\n \u00c7\u00f6z\u00fcm<\/strong>. A <\/em>\u015f\u00f6yle oynarsa daima kazan\u0131r: \u0130lk ad\u0131mda 1000 say\u0131s\u0131ndan 22 = 4 say\u0131s\u0131n\u0131 \u00e7\u0131kararak B\u2019ye 996 say\u0131s\u0131n\u0131 b\u0131rakmal\u0131. 996\u2019n\u0131n 6\u2019ya tam b\u00f6l\u00fcnebilen bir say\u0131 oldu\u011funa dikkat edelim, bunun \u00f6nemini az sonra a\u00e7\u0131klayaca\u011f\u0131z. A <\/em>sonraki ad\u0131mlar\u0131nda da B<\/em>\u2019den kalan say\u0131lardan 20 = 1, 21 = 2, 31 = 3, 22 = 4 veya 51 = 5 say\u0131lar\u0131n\u0131 \u00e7\u0131kararak B<\/em>\u2019ye hep 6\u2019ya tam b\u00f6l\u00fcnen bir say\u0131 b\u0131rak\u0131rsa B<\/em>\u2019den kalan say\u0131lar 6\u2019ya tam b\u00f6l\u00fcnmeyen say\u0131lar olacakt\u0131r. \u00c7\u00fcnk\u00fc a <\/em>asal, n <\/em>do\u011fal say\u0131 olmak \u00fczere a<\/em>n <\/em>say\u0131lar\u0131 6\u2019n\u0131n kat\u0131 olamaz. (Asallar aras\u0131nda 2\u2019den ba\u015fka \u00e7ift say\u0131 olmad\u0131\u011f\u0131ndan hi\u00e7bir asal\u0131n do\u011fal say\u0131 kuvveti 6\u2019n\u0131n kat\u0131 de\u011fildir) B\u00f6ylece A <\/em>kazan\u0131r, \u00e7\u00fcnk\u00fc oyun sonunda B<\/em>\u2019nin 0\u2019\u0131 elde edecek bir say\u0131y\u0131 \u00e7\u0131karmas\u0131 m\u00fcmk\u00fcn olmayacakt\u0131r.<\/p>\n Son k\u00e2\u011f\u0131t kazand\u0131r\u0131yor<\/strong><\/p>\n A <\/em>ve B <\/em>gibi iki oyuncu 50 adet k\u00e2\u011f\u0131tla \u015f\u00f6yle bir oyun oynuyorlar: A <\/em>ilk hamlesinde k\u00e2\u011f\u0131tlar\u0131 sadece diledi\u011fince iki desteye ay\u0131r\u0131yor. Sonras\u0131nda B<\/em>, bu destelerden birini oyun d\u0131\u015f\u0131nda b\u0131rakarak masan\u0131n kenar\u0131na koyuyor ve di\u011fer desteyi iki par\u00e7aya ay\u0131r\u0131yor. Bu kez A <\/em>da ayn\u0131 i\u015flemi yap\u0131yor, yani oyunda kalan son iki desteden birini oyun d\u0131\u015f\u0131nda b\u0131rak\u0131p di\u011ferini iki par\u00e7aya ay\u0131r\u0131yor. Oyun s\u0131ras\u0131yla bu \u015fekilde devam ediyor ve son k\u00e2\u011f\u0131d\u0131 alan oyunu kazan\u0131yor.<\/p>\n Bu oyunu hangi oyuncu nas\u0131l oynarsa kazan\u0131r?<\/p>\n \u00c7\u00f6z\u00fcm<\/strong>. Bu oyunu da A <\/em>\u015f\u00f6yle oynarsa kazan\u0131r: A<\/em>\u2019n\u0131n amac\u0131 B<\/em>\u2019nin son hamlesini yapaca\u011f\u0131 iki destenin 2 ve 3 k\u00e2\u011f\u0131ttan olu\u015fmas\u0131n\u0131 sa\u011flamak olmal\u0131, \u00e7\u00fcnk\u00fc e\u011fer B\u2019nin \u00f6n\u00fcnde 2 ve 3 k\u00e2\u011f\u0131ttan olu\u015fan iki deste varsa son hamlesini yapt\u0131ktan sonra mutlaka 1 k\u00e2\u011f\u0131tl\u0131k bir par\u00e7a olacakt\u0131r. Bu durumda A<\/em>, 1 k\u00e2\u011f\u0131tl\u0131k par\u00e7ay\u0131 oyun d\u0131\u015f\u0131nda b\u0131rak\u0131p di\u011fer destedeki k\u00e2\u011f\u0131tlar\u0131 alarak oyunu kazanm\u0131\u015f olur.<\/p>\n \u015eimdi oyunun ba\u015f\u0131na d\u00f6nelim ve A<\/em>\u2019n\u0131n oyun sonunda B<\/em>\u2019nin \u00f6n\u00fcne 2 ve 3 k\u00e2\u011f\u0131ttan olu\u015fan 2 desteyi koymay\u0131 nas\u0131l ba\u015faraca\u011f\u0131n\u0131 g\u00f6relim. Ba\u015flang\u0131\u00e7ta A, 50 k\u00e2\u011f\u0131tl\u0131k desteyi 5\u2019le b\u00f6l\u00fcnd\u00fcklerinde 2 ve 3 kalan\u0131n\u0131 veren iki desteye ay\u0131rmal\u0131. \u00d6rne\u011fin 22 ve 28\u2019lik iki deste olabilir. Bundan sonra B<\/em>\u2019nin hamlesiyle olu\u015facak destelerden en az birindeki k\u00e2\u011f\u0131t say\u0131s\u0131 5\u2019le b\u00f6l\u00fcnd\u00fc\u011f\u00fcnde 0, 1 veya 4 kalan\u0131n\u0131 verecektir. Art\u0131k A<\/em>, bu a\u015famadan sonra \u00f6n\u00fcne koyulan iki desteden birini oyun d\u0131\u015f\u0131nda b\u0131rakacak, di\u011ferini de 5\u2019le b\u00f6l\u00fcnd\u00fc\u011f\u00fcnde 3 ve 2, 3 ve 3 veya 2 ve 2 kalan\u0131n\u0131 veren say\u0131daki iki desteye ay\u0131racakt\u0131r. B\u00f6ylece son hamlede B\u2019nin \u00f6n\u00fcnde 2 ve 3 k\u00e2\u011f\u0131ttan olu\u015fan iki deste kalm\u0131\u015f olacak ve A <\/em>kazanacakt\u0131r.<\/p>\n","protected":false},"excerpt":{"rendered":" Matematiksel d\u00fc\u015f\u00fcnmenin zarafetiyle dolu \u00fc\u00e7 g\u00fczel oyunu \u00e7\u00f6z\u00fcmleriyle birlikte payla\u015f\u0131yorum. Say\u0131 tahmin oyunu Arkada\u015f\u0131n\u0131z k\u00e2\u011f\u0131da yazd\u0131\u011f\u0131 iki basamakl\u0131 do\u011fal say\u0131y\u0131 tahmin etmenizi istiyor. Her tahmin sonras\u0131nda do\u011fru olan basamak say\u0131s\u0131n\u0131 0, 1 ve 2 rakamlar\u0131ndan biriyle s\u00f6yleyece\u011fini bildiriyor. \u00d6rne\u011fin, k\u00e2\u011f\u0131tta 54 yaz\u0131l\u0131 ve siz 24 dediniz. Arkada\u015f\u0131n\u0131z \u201c1\u201d diyor, sonras\u0131nda 45 dediyseniz bu kez hi\u00e7bir […]<\/p>\n","protected":false},"author":375,"featured_media":16394,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[181,25,514],"tags":[1932,208,1572,1530],"class_list":["post-16393","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-144-sayi","category-matematik","category-matematik-sohbetleri","tag-beyin-jimnastigi","tag-matematik","tag-problemler","tag-sayilar"],"acf":[],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t