{"id":32,"date":"2010-07-14T13:29:20","date_gmt":"2010-07-14T17:29:20","guid":{"rendered":"http:\/\/mathriddles.williams.edu\/?p=32"},"modified":"2025-01-27T09:41:31","modified_gmt":"2025-01-27T14:41:31","slug":"give-me-a-hand","status":"publish","type":"post","link":"https:\/\/sites.williams.edu\/mathriddles\/difficulty\/medium\/give-me-a-hand\/","title":{"rendered":"Give Me a Hand"},"content":{"rendered":"<p>A professor and their spouse are at a party. At the party there are four more couples (overall five couples).<\/p>\n<p>During the party couples shake hands with the following rules:<br \/>\na. One does not shake hands with oneself.<br \/>\nb. One does not shake his\/her spouse&#8217;s hand.<\/p>\n<p>At the end of the party the professor asked all the other guests at the party (including their spouse) how many different people they shook hands with. Each person tells him a different answer (meaning, if one person said &#8220;five,&#8221; no one else said &#8220;five&#8221;).<\/p>\n<p>With how many people did the professor shake hands?<\/p>\n<p>Communicated by Michael Geike (who heard it in college in 1999).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A professor and their spouse are at a party. At the party there are four more couples (overall five couples). During the party couples shake hands with the following rules: a. One does not shake hands with oneself. b. One does not shake his\/her spouse&#8217;s hand. At the end of the party the professor asked&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":[12,7],"tags":[],"class_list":["post-32","post","type-post","status-publish","format-standard","hentry","category-combinatorics","category-medium"],"acf":[],"_links":{"self":[{"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts\/32","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=32"}],"version-history":[{"count":1,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts\/32\/revisions"}],"predecessor-version":[{"id":1101,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts\/32\/revisions\/1101"}],"wp:attachment":[{"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/media?parent=32"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/categories?post=32"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/tags?post=32"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}