{"id":35193,"date":"2019-10-31T22:02:53","date_gmt":"2019-10-31T19:02:53","guid":{"rendered":"https:\/\/prohoster.info\/blog\/matematika-i-igra-set\/"},"modified":"2019-10-31T22:02:53","modified_gmt":"2019-10-31T19:02:53","slug":"matematika-i-igra-set","status":"publish","type":"post","link":"https:\/\/prohoster.info\/hu\/blog\/news\/matematika-i-igra-set","title":{"rendered":"Matematika \u00e9s a \u201eSet\u201d j\u00e1t\u00e9k.","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"<p><img decoding=\"async\" alt=\"Matematika \u00e9s a \u201eSet\u201d j\u00e1t\u00e9k.\" src=\"\/wp-content\/uploads\/2019\/06\/310b9e73ac15cf3185a7e060ad36dca8.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Aki tal\u00e1l itt egy 'set'-et, t\u0151lem kap egy csokol\u00e1d\u00e9t.<\/i><\/p>\n<p>A set egy zseni\u00e1lis j\u00e1t\u00e9k, amivel k\u00f6r\u00fclbel\u00fcl 5 \u00e9ve j\u00e1tszottunk. Kiab\u00e1l\u00e1sok, \u00fcv\u00f6lt\u00e9sek, a kombin\u00e1ci\u00f3k lefot\u00f3z\u00e1sa. <\/p>\n<p>A j\u00e1t\u00e9k szab\u00e1lyai szerint 1991-ben Marsha Falco genetikus tal\u00e1lta fel, amikor a n\u00e9met juh\u00e1szok epilepszi\u00e1j\u00e1nak kutat\u00e1sa sor\u00e1n jegyzetelt 1974-ben. Azok sz\u00e1m\u00e1ra, akiknek az agyuk el\u00e9gg\u00e9 meg van terhelve a matematik\u00e1val, egy id\u0151 ut\u00e1n felmer\u00fcl a gyan\u00fa, hogy itt valami a s\u00edkgeometri\u00e1val \u00e9s a pontok k\u00f6z\u00f6tti egyenesek h\u00faz\u00e1s\u00e1val kapcsolatos. (K\u00e9t megadott k\u00e1rty\u00e1hoz l\u00e9tezik egy \u00e9s csak egy k\u00e1rtya, ami vel\u00fck egy\u00fctt k\u00e9pezi a setet.)<br \/>\n<noindex><a rel=\"nofollow\" name=\"habracut\"><\/a><\/noindex><br \/>\n<img decoding=\"async\" alt=\"Matematika \u00e9s a \u201eSet\u201d j\u00e1t\u00e9k.\" src=\"\/wp-content\/uploads\/2019\/06\/33cc906d4936e3fa25238ba28c6fcfe7.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Marsha Falco mintha azt k\u00e9rdezn\u00e9: \"Na, nem tal\u00e1ltad meg a 'set'-et?\"<\/i><\/p>\n<h3>Eml\u00e9kezz\u00fcnk a szab\u00e1lyokra<\/h3>\n<p>\n<img decoding=\"async\" alt=\"Matematika \u00e9s a \u201eSet\u201d j\u00e1t\u00e9k.\" src=\"\/wp-content\/uploads\/2019\/06\/31a494ebd8dbccd27454d46d3c0e3ec8.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\nA set egy k\u00e1rtyaj\u00e1t\u00e9k. Minden k\u00e1rty\u00e1nak n\u00e9gy param\u00e9tere van, mindegyik h\u00e1rom \u00e9rt\u00e9ket vehet fel (\u00f6sszesen 3 x 3 \u00d7 3 \u00d7 3 = 81 k\u00e1rtya). <\/p>\n<p><img decoding=\"async\" alt=\"Matematika \u00e9s a \u201eSet\u201d j\u00e1t\u00e9k.\" src=\"\/wp-content\/uploads\/2019\/06\/75978b83104a01c548f251065470af2a.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<br \/>\nA param\u00e9terek t\u00edpusa \u00e9s \u00e9rtelmez\u00e9se a k\u00f6vetkez\u0151:<\/p>\n<ul>\n<li>alak ::= ellipszis | rombusz | 'ny\u00fal\u00f3s'<\/li>\n<li>sz\u00edn ::= piros | z\u00f6ld | lila<\/li>\n<li>t\u00f6lt\u00e9s ::= feh\u00e9r | cs\u00edkos | egysz\u00edn\u0171<\/li>\n<li>mennyis\u00e9g ::= 1 | 2 | 3<\/li>\n<\/ul>\n<p>\n<b>A j\u00e1t\u00e9k c\u00e9lja<\/b> abban \u00e1ll, hogy k\u00fcl\u00f6nleges h\u00e1rom k\u00e1rty\u00e1s kombin\u00e1ci\u00f3kat tal\u00e1ljunk. H\u00e1rom k\u00e1rty\u00e1t 'setnek' nevez\u00fcnk, ha a n\u00e9gy attrib\u00fatum k\u00f6z\u00fcl minden \u00e9rt\u00e9k azonos, vagy <i>mindent<\/i> k\u00fcl\u00f6nb\u00f6z\u0151.<\/p>\n<p><img decoding=\"async\" alt=\"Matematika \u00e9s a \u201eSet\u201d j\u00e1t\u00e9k.\" src=\"\/wp-content\/uploads\/2019\/06\/004f2a2bdc76f6952c078c5f51415484.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<br \/>\nM\u00e1s sz\u00f3val, h\u00e1rom k\u00e1rtya nem alkothat setet, ha k\u00e9t k\u00e1rtya ugyanazt az \u00e9rt\u00e9ket osztja meg egy param\u00e9terben, m\u00edg a harmadik m\u00e1s \u00e9rt\u00e9k\u0171. L\u00e1thatjuk, hogy b\u00e1rmely k\u00e9t k\u00e1rtya sz\u00e1m\u00e1ra mindig l\u00e9tezik egy harmadik (r\u00e1ad\u00e1sul egyetlen), amivel setet alkotnak.<\/p>\n<p><b>A j\u00e1t\u00e9k menete:<\/b> a vezet\u0151 12 k\u00e1rty\u00e1t helyez az asztalra. Amikor valaki setet tal\u00e1l, kiab\u00e1lja: 'Set!' \u00e9s nyugodtan elviszi a setet alkot\u00f3 k\u00e1rty\u00e1kat. Ha viszont a kirakott k\u00e1rty\u00e1k k\u00f6z\u00f6tt nincs set (val\u00f3sz\u00edn\u0171leg csak \u00fagy t\u0171nik, hogy nincs), a vezet\u0151 tov\u00e1bbi h\u00e1rom k\u00e1rty\u00e1t rak ki.<\/p>\n<p>A set n\u00e9lk\u00fcli maxim\u00e1lis k\u00e1rtyasz\u00e1m 20. A k\u00f6r addig folytat\u00f3dik, am\u00edg a pakli ki nem mer\u00fcl. Az nyer, aki t\u00f6bb setet gy\u0171jt\u00f6tt.<\/p>\n<p>A matematikusok nem t\u00e9tlenkedtek \u00e9s 20 k\u00e1rty\u00e1s kombin\u00e1ci\u00f3t \u00e1ll\u00edtottak \u00f6ssze. Aki Chuck Norrisnak \u00e9rzi mag\u00e1t, elfelejtheti ezt a k\u00e9pet, \u00e9s megpr\u00f3b\u00e1lhat sansz n\u00e9lk\u00fcl \u00f6sszerakni egy 'pascient'.<br \/>\nVagy esetleg ellen\u0151rizheti, hogy h\u00e1tha m\u00e9gis van itt 'set'?<\/p>\n<h3>20 k\u00e1rtya set n\u00e9lk\u00fcl<\/h3>\n<p>\n<img decoding=\"async\" alt=\"Matematika \u00e9s a \u201eSet\u201d j\u00e1t\u00e9k.\" src=\"\/wp-content\/uploads\/2019\/06\/0e939d2d5ac475941ac6cc798d99ec5f.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>K\u00e9nyelmes ellen\u0151rizni, hogy nincs 'set sz\u00ednben'.<\/i><\/p>\n<p><img decoding=\"async\" alt=\"Matematika \u00e9s a \u201eSet\u201d j\u00e1t\u00e9k.\" src=\"\/wp-content\/uploads\/2019\/06\/914b852fe424faf4bc06230d8e110b8d.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<br \/>\n<i>Ugyanazok a k\u00e1rty\u00e1k, de a helyez\u00e9s azt mutatja, hogy nincs set 't\u00f6lt\u00e9s' param\u00e9terben.<\/i><\/p>\n<p><img decoding=\"async\" alt=\"Matematika \u00e9s a \u201eSet\u201d j\u00e1t\u00e9k.\" src=\"\/wp-content\/uploads\/2019\/06\/70cc65fab552c5215ce9c6d5342d9bc9.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<br \/>\n<i>Mennyis\u00e9g alapj\u00e1n.<\/i><\/p>\n<p><img decoding=\"async\" alt=\"Matematika \u00e9s a \u201eSet\u201d j\u00e1t\u00e9k.\" src=\"\/wp-content\/uploads\/2019\/06\/548664a37ac483a166b0f33f8bdd941d.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<br \/>\n<i>Alakok szerint.<\/i><\/p>\n<p><img decoding=\"async\" alt=\"Matematika \u00e9s a \u201eSet\u201d j\u00e1t\u00e9k.\" src=\"\/wp-content\/uploads\/2019\/06\/418a8252c7d4d182087c3e667f4c491b.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<br \/>\n<i>Nincs set a jellemz\u0151k elt\u00e9r\u00e9se szerint.<\/i><\/p>\n<h3>Nyitott, megoldatlan matematikai feladat<\/h3>\n<p>\nH\u00e1ny k\u00e1rty\u00e1t lehet maxim\u00e1lisan lerakni, hogy ne j\u00f6jj\u00f6n l\u00e9tre egyetlen 'set' sem? A jel\u00f6l\u00e9s h\u00e1rom \u00e9rt\u00e9ket vehet fel.<\/p>\n<p>1 'jel\u00f6l\u00e9s' eset\u00e9n \u2014 2 k\u00e1rtya<br \/>\n2 jel\u00f6l\u00e9s \u2014 4 k\u00e1rtya<br \/>\n3 jel\u00f6l\u00e9s \u2014 9 k\u00e1rtya<br \/>\n4 jel\u00f6l\u00e9s \u2014 20 k\u00e1rtya<br \/>\n5 jel\u00f6l\u00e9s \u2014 45 k\u00e1rtya<br \/>\n6 jel\u00f6l\u00e9s \u2014 112 k\u00e1rtya<br \/>\n7 jel\u00f6l\u00e9s \u2014 <i>nem tudom<\/i><\/p>\n<p>\u00c9s mi a helyzet 'n\u2192\u221e'-val?<\/p>\n<h3>Video<\/h3>\n<p>\nA j\u00e1t\u00e9k l\u00e9trehoz\u00f3ja:<\/p>\n<p><center><div class=\"youtube-placeholder\" data-id=\"7AeEr9QtDF0\" onclick=\"loadVideo(this)\">\r\n        <img decoding=\"async\" src=\"https:\/\/img.youtube.com\/vi\/7AeEr9QtDF0\/hqdefault.jpg\" alt=\"Vide\u00f3 lej\u00e1tsz\u00e1sa\" loading=\"lazy\" width=\"480\" height=\"360\" style=\"width:100%;height:auto;\">\r\n        <div class=\"play-button\"><\/div>\r\n    <\/div><\/center><br \/>\nAlekszej Szavvatejev szellemesen mes\u00e9l a 'Set'-r\u0151l:<\/p>\n<p><center><div class=\"youtube-placeholder\" data-id=\"vwIO-kzvY5Q\" onclick=\"loadVideo(this)\">\r\n        <img decoding=\"async\" src=\"https:\/\/img.youtube.com\/vi\/vwIO-kzvY5Q\/hqdefault.jpg\" alt=\"Vide\u00f3 lej\u00e1tsz\u00e1sa\" loading=\"lazy\" width=\"480\" height=\"360\" style=\"width:100%;height:auto;\">\r\n        <div class=\"play-button\"><\/div>\r\n    <\/div><\/center><\/p>\n<h3>Cikkek<\/h3>\n<p><\/p>\n<ul>\n<li><noindex><a rel=\"nofollow\" href=\"http:\/\/pbg.cs.illinois.edu\/papers\/set.pdf\">A J\u00c1T\u00c9K BONYOLULTS\u00c1GA A 'SET'-BEN<\/a><\/noindex><\/li>\n<li><noindex><a rel=\"nofollow\" href=\"https:\/\/henrikwarne.com\/2011\/09\/30\/set-probabilities-revisited\/\">A 'SET' Val\u00f3sz\u00edn\u0171s\u00e9gei \u00dajra\u00e9rtelmezve<\/a><\/noindex><\/li>\n<li><noindex><a rel=\"nofollow\" href=\"https:\/\/homepages.warwick.ac.uk\/staff\/D.Maclagan\/papers\/set.pdf\">A K\u00c1RTYAJ\u00c1T\u00c9K 'SET'<\/a><\/noindex><\/li>\n<li><noindex><a rel=\"nofollow\" href=\"https:\/\/digitalcommons.ric.edu\/cgi\/viewcontent.cgi?referer=&amp;httpsredir=1&amp;article=1094&amp;context=honors_projects\">A K\u00c1RTYAJ\u00c1T\u00c9K 'SET' MATEMATIK\u00c1JA<\/a><\/noindex><\/li>\n<\/ul>\n<p>Forr\u00e1s: <a content=\"nofollow\" rel=\"nofollow\" href=\"https:\/\/habr.com\/ru\/post\/455634\/\">habr.com<\/a><\/p>","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"<p>\u041a\u0442\u043e \u043d\u0430\u0439\u0434\u0435\u0442 \u0442\u0443\u0442 \u00ab\u0441\u0435\u0442\u00bb, \u043f\u043e\u043b\u0443\u0447\u0438\u0442 \u043e\u0442 \u043c\u0435\u043d\u044f \u0448\u043e\u043a\u043e\u043b\u0430\u0434\u043a\u0443. \u0421\u0435\u0442 \u2014 \u0433\u0435\u043d\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0438\u0433\u0440\u0430 \u0432 \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043c\u044b \u0440\u0443\u0431\u0438\u043b\u0438\u0441\u044c \u043b\u0435\u0442 5 \u043d\u0430\u0437\u0430\u0434. \u041a\u0440\u0438\u043a\u0438, \u0432\u043e\u043f\u043b\u0438, \u0444\u043e\u0442\u043e\u0433\u0440\u0430\u0444\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0439. \u0412 \u043f\u0440\u0430\u0432\u0438\u043b\u0430\u0445 \u0438\u0433\u0440\u044b \u043d\u0430\u043f\u0438\u0441\u0430\u043d\u043e, \u0447\u0442\u043e \u0435\u0435 \u0438\u0437\u043e\u0431\u0440\u0435\u043b\u0430 \u0432 1991 \u0433\u043e\u0434\u0443 \u0433\u0435\u043d\u0435\u0442\u0438\u043a \u041c\u0430\u0440\u0448\u0430 \u0424\u0430\u043b\u043a\u043e (Marsha Falco), \u0434\u0435\u043b\u0430\u044f \u043f\u043e\u043c\u0435\u0442\u043a\u0438 \u0432\u043e \u0432\u0440\u0435\u043c\u044f \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u044f \u044d\u043f\u0438\u043b\u0435\u043f\u0441\u0438\u0438 \u0443 \u043d\u0435\u043c\u0435\u0446\u043a\u0438\u0445 \u043e\u0432\u0447\u0430\u0440\u043e\u043a \u0432 1974 \u0433\u043e\u0434\u0443. \u0414\u043b\u044f \u0442\u0435\u0445, \u0443 \u043a\u043e\u0433\u043e \u043c\u043e\u0437\u0433 [&hellip;]<\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":26448,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[702],"tags":[],"class_list":["post-35193","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-news"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.3 - aioseo.com -->\n\t<meta name=\"description\" content=\"\u041a\u0442\u043e \u043d\u0430\u0439\u0434\u0435\u0442 \u0442\u0443\u0442 \u00ab\u0441\u0435\u0442\u00bb, \u043f\u043e\u043b\u0443\u0447\u0438\u0442 \u043e\u0442 \u043c\u0435\u043d\u044f \u0448\u043e\u043a\u043e\u043b\u0430\u0434\u043a\u0443. .\" \/>\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<meta name=\"author\" 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