{"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\/en\/blog\/news\/matematika-i-igra-set","title":{"rendered":"Mathematics and the game \"Set\"","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"<p><img decoding=\"async\" alt=\"Mathematics and the game &quot;Set&quot;\" src=\"\/wp-content\/uploads\/2019\/06\/310b9e73ac15cf3185a7e060ad36dca8.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Whoever finds a 'set' here will get a chocolate from me.<\/i><\/p>\n<p>'Set' is a brilliant game that we played about 5 years ago. Shouts, screams, photographing combinations. <\/p>\n<p>The game's rules state that it was invented in 1991 by geneticist Marsha Falco, who made notes while researching epilepsy in German shepherds in 1974. For those whose brains are sufficiently exhausted by mathematics, there eventually arises a suspicion that there are echoes of planar geometry and drawing lines through points. (For any two cards there is exactly one card that forms a set with them.)<br \/>\n<noindex><a rel=\"nofollow\" name=\"habracut\"><\/a><\/noindex><br \/>\n<img decoding=\"async\" alt=\"Mathematics and the game &quot;Set&quot;\" src=\"\/wp-content\/uploads\/2019\/06\/33cc906d4936e3fa25238ba28c6fcfe7.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Marsha Falco seemingly asks: 'So, didn\u2019t you find the \u201cset\u201d?'<\/i><\/p>\n<h3>Let\u2019s recall the rules<\/h3>\n<p>\n<img decoding=\"async\" alt=\"Mathematics and the game &quot;Set&quot;\" src=\"\/wp-content\/uploads\/2019\/06\/31a494ebd8dbccd27454d46d3c0e3ec8.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n'Set' is a card game. All cards have four parameters, each of which can have three values (thus 3 x 3 x 3 x 3 = 81 cards). <\/p>\n<p><img decoding=\"async\" alt=\"Mathematics and the game &quot;Set&quot;\" src=\"\/wp-content\/uploads\/2019\/06\/75978b83104a01c548f251065470af2a.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<br \/>\nThe types and values of the parameters are as follows:<\/p>\n<ul>\n<li>shape ::= ellipse | diamond | 'squiggle'<\/li>\n<li>color ::= red | green | purple<\/li>\n<li>shading ::= solid | striped | open<\/li>\n<li>number ::= 1 | 2 | 3<\/li>\n<\/ul>\n<p>\n<b>The goal of the game<\/b> is to find special combinations of three cards. Three cards are called a 'set' if for each of the four attributes, the cards are either all the same or <i>all<\/i> all different.<\/p>\n<p><img decoding=\"async\" alt=\"Mathematics and the game &quot;Set&quot;\" src=\"\/wp-content\/uploads\/2019\/06\/004f2a2bdc76f6952c078c5f51415484.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<br \/>\nIn other words, three cards do not form a set if two cards have one value for a parameter and the third card has a different value. It can be seen that for any two cards, there will always be a third (and only one) that forms a set with them.<\/p>\n<p><b>Game play:<\/b> the dealer lays out 12 cards. When someone finds a set, they shout 'Set!' and then calmly take the cards that make up the set. If there\u2019s no set among the laid out cards (it often seems that there isn\u2019t), the dealer lays out three more cards.<\/p>\n<p>The maximum number of cards without a set is 20. The round continues until the deck is depleted. The player who collects the most sets wins.<\/p>\n<p>Mathematicians have provided a combination of 20 cards. Anyone who considers themselves Chuck Norris can forget this picture and try to collect the 'solitaire' without a set on their own.<br \/>\nOr check if there might still be a 'set' here?<\/p>\n<h3>20 cards without a set<\/h3>\n<p>\n<img decoding=\"async\" alt=\"Mathematics and the game &quot;Set&quot;\" src=\"\/wp-content\/uploads\/2019\/06\/0e939d2d5ac475941ac6cc798d99ec5f.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>It's easy to check that there is no 'set by color'.<\/i><\/p>\n<p><img decoding=\"async\" alt=\"Mathematics and the game &quot;Set&quot;\" src=\"\/wp-content\/uploads\/2019\/06\/914b852fe424faf4bc06230d8e110b8d.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<br \/>\n<i>The same cards, but the arrangement shows no sets by the 'shading' parameter.<\/i><\/p>\n<p><img decoding=\"async\" alt=\"Mathematics and the game &quot;Set&quot;\" src=\"\/wp-content\/uploads\/2019\/06\/70cc65fab552c5215ce9c6d5342d9bc9.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<br \/>\n<i>By number.<\/i><\/p>\n<p><img decoding=\"async\" alt=\"Mathematics and the game &quot;Set&quot;\" src=\"\/wp-content\/uploads\/2019\/06\/548664a37ac483a166b0f33f8bdd941d.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<br \/>\n<i>By shapes.<\/i><\/p>\n<p><img decoding=\"async\" alt=\"Mathematics and the game &quot;Set&quot;\" src=\"\/wp-content\/uploads\/2019\/06\/418a8252c7d4d182087c3e667f4c491b.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<br \/>\n<i>No set by attribute differences.<\/i><\/p>\n<h3>An open unresolved problem in mathematics<\/h3>\n<p>\nWhat is the maximum number of cards that can be laid out without forming a single 'set'? The attribute has three values.<\/p>\n<p>with 1 'attribute' \u2014 2 cards<br \/>\n2 attributes \u2014 4 cards<br \/>\n3 attributes \u2014 9 cards<br \/>\n4 attributes \u2014 20 cards<br \/>\n5 attributes \u2014 45 cards<br \/>\n6 attributes \u2014 112 cards<br \/>\n7 attributes \u2014 <i>unknown<\/i><\/p>\n<p>And when n \u2192 \u221e?<\/p>\n<h3>Video<\/h3>\n<p>\nGame creator:<\/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=\"Play video\" loading=\"lazy\" width=\"480\" height=\"360\" style=\"width:100%;height:auto;\">\r\n        <div class=\"play-button\"><\/div>\r\n    <\/div><\/center><br \/>\nAlexey Savvateev brilliantly explains the game of Set:<\/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=\"Play video\" 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>Articles<\/h3>\n<p><\/p>\n<ul>\n<li><noindex><a rel=\"nofollow\" href=\"http:\/\/pbg.cs.illinois.edu\/papers\/set.pdf\">ON THE COMPLEXITY OF THE GAME OF SET<\/a><\/noindex><\/li>\n<li><noindex><a rel=\"nofollow\" href=\"https:\/\/henrikwarne.com\/2011\/09\/30\/set-probabilities-revisited\/\">SET Probabilities Revisited<\/a><\/noindex><\/li>\n<li><noindex><a rel=\"nofollow\" href=\"https:\/\/homepages.warwick.ac.uk\/staff\/D.Maclagan\/papers\/set.pdf\">THE CARD GAME 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\">The Mathematics of the Card Game Set<\/a><\/noindex><\/li>\n<\/ul>\n<p>Source: <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 5.0.1.1 - 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\" content=\"Yuri Gagarin\"\/>\n\t<link rel=\"canonical\" href=\"https:\/\/prohoster.info\/en\/blog\/news\/matematika-i-igra-set\" 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