{"id":64,"date":"2010-07-13T15:58:56","date_gmt":"2010-07-13T15:58:56","guid":{"rendered":"http:\/\/mathriddles.williams.edu\/?p=64"},"modified":"2025-01-27T09:41:32","modified_gmt":"2025-01-27T14:41:32","slug":"hats-off","status":"publish","type":"post","link":"https:\/\/sites.williams.edu\/mathriddles\/difficulty\/medium\/hats-off\/","title":{"rendered":"Hats Off"},"content":{"rendered":"<p>Three mathematicians are applying for a job. There are five hats, three white, two black. They&#8217;re lined up, and a hat is placed on each.  The first person in line cannot see any hat; the second in line sees only the hat of the person in front of him; the third person sees only the hats of the two people in front of her. The first person to correctly figure out what color hat he has gets the job; you guess wrong and you are killed. Assume these are INTELLIGENT mathematicians, and that they will do the logically correct thing at each stage &#8212; if something can be deduced, they will figure it out. After a long pause, the first person, who cannot see any hats, says he knows the color of his hat. What is the color, and how does he know? <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Three mathematicians are applying for a job. There are five hats, three white, two black. They&#8217;re lined up, and a hat is placed on each. The first person in line cannot see any hat; the second in line sees only the hat of the person in front of him; the third person sees only the&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":[12,16,7],"tags":[],"class_list":["post-64","post","type-post","status-publish","format-standard","hentry","category-combinatorics","category-hat","category-medium"],"acf":[],"_links":{"self":[{"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts\/64","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=64"}],"version-history":[{"count":1,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts\/64\/revisions"}],"predecessor-version":[{"id":1184,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts\/64\/revisions\/1184"}],"wp:attachment":[{"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/media?parent=64"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/categories?post=64"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/tags?post=64"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}