{"id":113,"date":"2010-07-13T18:50:06","date_gmt":"2010-07-13T18:50:06","guid":{"rendered":"http:\/\/mathriddles.williams.edu\/?p=113"},"modified":"2025-01-27T09:41:32","modified_gmt":"2025-01-27T14:41:32","slug":"three-hats-and-a-strange-probability","status":"publish","type":"post","link":"https:\/\/sites.williams.edu\/mathriddles\/difficulty\/hard\/three-hats-and-a-strange-probability\/","title":{"rendered":"Three Hats and a Strange Probability"},"content":{"rendered":"<p>Three players enter a room and a red or blue hat is placed on each person&#8217;s head. The color of each hat is determined by a coin toss, with the outcome of one coin toss having no effect on the others. Each person can see the other players&#8217; hats but not his own.<\/p>\n<p>No communication of any sort is allowed, except for an initial strategy session before the game begins. Once they have had a chance to look at the other hats, the players must simultaneously guess the color of their own hats or pass. The group shares a hypothetical $3 million prize if at least one player guesses correctly and no players guess incorrectly.<\/p>\n<p>The same game can be played with any number of players. The general problem is to find a strategy for the group that maximizes its chances of winning the prize.<\/p>\n<p>Communicated by Jim Vere.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Three players enter a room and a red or blue hat is placed on each person&#8217;s head. The color of each hat is determined by a coin toss, with the outcome of one coin toss having no effect on the others. Each person can see the other players&#8217; hats but not his own. No communication&hellip;<\/p>\n","protected":false},"author":2861,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[12,6,16,19],"tags":[],"class_list":["post-113","post","type-post","status-publish","format-standard","hentry","category-combinatorics","category-hard","category-hat","category-probability"],"acf":[],"_links":{"self":[{"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts\/113","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/users\/2861"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/comments?post=113"}],"version-history":[{"count":1,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts\/113\/revisions"}],"predecessor-version":[{"id":1167,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts\/113\/revisions\/1167"}],"wp:attachment":[{"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/media?parent=113"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/categories?post=113"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/tags?post=113"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}