Problemlerin saf d\u00fcnyas\u0131na dal\u0131p gitmek ruh sa\u011fl\u0131\u011f\u0131na iyi geliyor. D\u00fc\u015f\u00fcnmek, anlamaya \u00e7al\u0131\u015fmak, ke\u015ffetmek, \u00e7\u00f6zememenin s\u0131k\u0131nt\u0131s\u0131, \u00e7\u00f6zmenin sevinci\u2026 Kolektif mutsuzlu\u011fu ya\u015fad\u0131\u011f\u0131m\u0131z \u015fu g\u00fcnlerde a\u015fa\u011f\u0131daki problemlerle u\u011fra\u015fan okurlar\u0131m\u0131z\u0131n en az\u0131ndan u\u011fra\u015fma s\u00fcresince kendilerini daha iyi hissedeceklerine inan\u0131yorum. Ayr\u0131ca, problemlerin \u00e7\u00f6z\u00fcm\u00fc i\u00e7in sadece temel aritmetik bilgisinin yeterli olaca\u011f\u0131n\u0131 da belirtmek isterim.<\/p>\n
Hik\u00e2ye.<\/strong> Bir yazar hik\u00e2yesini bitirdi\u011finde g\u00fcnl\u00fc\u011f\u00fcne bakarak \u015fu c\u00fcmleleri s\u00f6yler:<\/p>\n Yazar bu hik\u00e2yeyi ka\u00e7 g\u00fcnde bitirmi\u015ftir?<\/p>\n Son say\u0131. <\/strong>Bir k\u00e2\u011f\u0131da 1 ile 121 aras\u0131ndaki \u00e7ift say\u0131lar\u0131 yazd\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m: 2, 4, 6, 8, 10, \u2026 120. Bu say\u0131lardan herhangi ikisini silip, yerine sildi\u011fimiz say\u0131lar\u0131n toplam\u0131n\u0131n 1 fazlas\u0131n\u0131 yaz\u0131yoruz. Bu i\u015fleme k\u00e2\u011f\u0131tta bir tane say\u0131 kalana kadar devem edersek son say\u0131 ka\u00e7 olur?<\/p>\n \u0130ki kat\u0131n\u0131 ve karesini alma. <\/strong>1 say\u0131s\u0131na \u201c2 kat ve kare alma\u201d i\u015flemleri uygulayarak en az ka\u00e7 ad\u0131mda\u00a0251<\/sup>\u00a0say\u0131s\u0131 elde edilebilir? ( \u00d6rne\u011fin 25<\/sup>\u00a0say\u0131s\u0131na\u00a01 – 2 – 22<\/sup> – 24<\/sup> – 25<\/sup> \u00a0\u015feklinde en az 4 ad\u0131mda ula\u015f\u0131l\u0131yor.)<\/p>\n En \u00e7ok bilye say\u0131s\u0131. <\/strong>D\u00f6rt farkl\u0131 torbadaki bilyelerin toplam say\u0131s\u0131 120\u2019dir. Ayr\u0131ca, herhangi iki torbadaki bilyelerin say\u0131lar\u0131 aras\u0131ndaki fark\u0131n 8\u2019den \u00e7ok 29\u2019dan az oldu\u011fu bilindi\u011fine g\u00f6re en \u00e7ok bilye bulunan kutudaki bilye say\u0131s\u0131 en \u00e7ok ka\u00e7t\u0131r?<\/p>\n Hangi ev? <\/strong>Sahilde in\u015fa edilmi\u015f 17 evden birinde oturan bir ki\u015fi \u015fu c\u00fcmleleri kuruyor: \u201cDenize bakarak sa\u011f\u0131mdaki ev say\u0131s\u0131yla solumdaki ev say\u0131s\u0131n\u0131 \u00e7arpt\u0131\u011f\u0131m zaman, sol kom\u015fumun ayn\u0131 i\u015flemi yapt\u0131\u011f\u0131nda elde etti\u011fi say\u0131dan 7 fazlas\u0131n\u0131 elde ediyorum.\u201d Bu ki\u015fi soldan ka\u00e7\u0131nc\u0131 evde oturuyor?<\/p>\n \u015eampiyon kim? <\/strong>A,<\/em> B<\/em>, C<\/em>, D<\/em> ve E <\/em>gibi be\u015f ki\u015finin kat\u0131ld\u0131\u011f\u0131 bir satran\u00e7 turnuvas\u0131nda d\u00f6rt farkl\u0131 satran\u00e7 otoritesinin tahminleri a\u015fa\u011f\u0131daki gibidir:<\/p>\n Yukar\u0131daki tahminlerin sadece biri do\u011fru oldu\u011funa g\u00f6re kim \u015fampiyon olmu\u015ftur?<\/p>\n Ayn\u0131 ya\u015fta olanlar.<\/strong> \u0130kisi ayn\u0131 ya\u015fta olan 5 ki\u015fiden her biri kendisi d\u0131\u015f\u0131ndaki 4 ki\u015finin ya\u015flar\u0131n\u0131 toplad\u0131\u011f\u0131nda olu\u015fan 5 say\u0131dan ayn\u0131 olan iki say\u0131n\u0131n sadece biri yaz\u0131larak 115, 118, 123, 128 say\u0131lar\u0131 elde ediliyor. Ayn\u0131 ya\u015ftaki ki\u015filerin ya\u015f\u0131 ka\u00e7t\u0131r?<\/p>\n Turnuvadaki tak\u0131m say\u0131s\u0131. <\/strong>Bir turnuvada her tak\u0131m di\u011ferleriyle bir kez kar\u015f\u0131la\u015f\u0131yor. Tak\u0131mlardan biri 10 ma\u00e7 yapt\u0131ktan sonra turnuvadan \u00e7ekiliyor. Toplam 88 kar\u015f\u0131la\u015fma yap\u0131ld\u0131\u011f\u0131na g\u00f6re bu turnuvaya ka\u00e7 tak\u0131m kat\u0131lm\u0131\u015ft\u0131r?<\/p>\n Kuyruk.<\/strong> Bir kuyrukta bulunan A<\/em>, B<\/em> ve C <\/em>gibi \u00fc\u00e7 ki\u015fiden A<\/em>\u2019n\u0131n B<\/em> ile aras\u0131nda 11,C <\/em>ile aras\u0131nda 15 ki\u015fi vard\u0131r. B <\/em>ile C<\/em> aras\u0131ndaki ki\u015fi say\u0131s\u0131 A<\/em>\u2019n\u0131n hem ba\u015ftan hem sondan s\u0131ra say\u0131s\u0131na e\u015fitse C<\/em> ka\u00e7\u0131nc\u0131 s\u0131rada olabilir?<\/p>\n N\u00f6bet. <\/strong>Bir hekim 5 g\u00fcnde bir n\u00f6bet tutmaktad\u0131r. \u0130lk n\u00f6betini sal\u0131 g\u00fcn\u00fc tutuyor, ama n\u00f6bet tutma s\u0131ras\u0131 tekrar sal\u0131ya rastlad\u0131\u011f\u0131nda 4 g\u00fcnde bir n\u00f6bet tutmaya ba\u015fl\u0131yor.\u00a0 Sonraki n\u00f6beti yine sal\u0131ya geldi\u011finde 3 g\u00fcnde bir n\u00f6bet tutuyor. Bu \u015fekilde, n\u00f6bet tutu\u011fu her sal\u0131 iki n\u00f6bet aras\u0131ndaki s\u00fcreyi 1 g\u00fcn azalt\u0131yor. Bu hekim ka\u00e7 n\u00f6bet tutar?<\/p>\n \u00d6l\u00e7\u00fc. <\/strong>Silindir \u015feklinde camdan yap\u0131lm\u0131\u015f 6 litrelik iki kab\u0131m\u0131z var. Kaplardan ince ve uzun olan\u0131n\u0131n y\u00fcksekli\u011fi 9 birim, k\u0131sa ve geni\u015f olan\u0131n\u0131n y\u00fcksekli\u011fi 4 birim. Ayr\u0131ca, b\u00fcy\u00fck bir \u00fc\u00e7\u00fcnc\u00fc kab\u0131m\u0131z var. Bir musluktan istedi\u011fimiz kadar su alabilece\u011fimize g\u00f6re 4 litre suyu nas\u0131l \u00f6l\u00e7eriz?<\/p>\n \u201cD\u00fcn tam bu saatte buradayd\u0131k.\u201d <\/strong>\u0130ki arkada\u015f \u0130zmir\u2019den saat 6.00\u2019da hareket ederek 6 saatte Bursa\u2019ya var\u0131yorlar.<\/p>\n Ertesi g\u00fcn yine saat 6.00\u2019da Bursa\u2019dan \u0130zmir\u2019e hareket ederek 4 saat sonra \u0130zmir\u2019de oluyorlar. Arac\u0131n s\u00fcr\u00fcc\u00fcs\u00fc d\u00f6n\u00fc\u015f yolunda arkada\u015f\u0131na \u201cD\u00fcn tam bu saatte buradayd\u0131k.\u201d dedi\u011fi anda saat ka\u00e7t\u0131?<\/p>\n Not:\u00a0<\/strong>Yukar\u0131daki problemlerin en az 9 tanesinin \u00e7\u00f6z\u00fcm\u00fcn\u00fc 15. 02. 2017 tarihine kadar a_torun60@hotmail.com adresine g\u00f6nderen ilk iki okurumuza Ali Nesin\u2019le birlikte kaleme ald\u0131\u011f\u0131m Matematik\u00e7i Portreleri <\/em>isimli kitap hediye edilecek ve yan\u0131tlar \u00f6n\u00fcm\u00fczdeki say\u0131da verilecektir.<\/p>\n","protected":false},"excerpt":{"rendered":" Problemlerin saf d\u00fcnyas\u0131na dal\u0131p gitmek ruh sa\u011fl\u0131\u011f\u0131na iyi geliyor. D\u00fc\u015f\u00fcnmek, anlamaya \u00e7al\u0131\u015fmak, ke\u015ffetmek, \u00e7\u00f6zememenin s\u0131k\u0131nt\u0131s\u0131, \u00e7\u00f6zmenin sevinci\u2026 Kolektif mutsuzlu\u011fu ya\u015fad\u0131\u011f\u0131m\u0131z \u015fu g\u00fcnlerde a\u015fa\u011f\u0131daki problemlerle u\u011fra\u015fan okurlar\u0131m\u0131z\u0131n en az\u0131ndan u\u011fra\u015fma s\u00fcresince kendilerini daha iyi hissedeceklerine inan\u0131yorum. Ayr\u0131ca, problemlerin \u00e7\u00f6z\u00fcm\u00fc i\u00e7in sadece temel aritmetik bilgisinin yeterli olaca\u011f\u0131n\u0131 da belirtmek isterim. Hik\u00e2ye. Bir yazar hik\u00e2yesini bitirdi\u011finde g\u00fcnl\u00fc\u011f\u00fcne bakarak […]<\/p>\n","protected":false},"author":375,"featured_media":13954,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[193,25,514],"tags":[208,1572,1530],"class_list":["post-13953","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-156-sayi","category-matematik","category-matematik-sohbetleri","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\n
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