{"id":123,"date":"2010-07-13T18:57:19","date_gmt":"2010-07-13T18:57:19","guid":{"rendered":"http:\/\/mathriddles.williams.edu\/?p=123"},"modified":"2025-01-27T09:41:32","modified_gmt":"2025-01-27T14:41:32","slug":"how-to-pick-up-the-bucks","status":"publish","type":"post","link":"https:\/\/sites.williams.edu\/mathriddles\/difficulty\/medium\/how-to-pick-up-the-bucks\/","title":{"rendered":"How to Pick Up the Bucks"},"content":{"rendered":"<p>You have 2N coins of varying denominations (each is a non-negative real number) in a line. Players A and B take turns choosing one coin from either end. Prove A always has a strategy that ensures he end up with at least as much as B.<\/p>\n<p>Communicated by A. Roy<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-medium wp-image-467\" src=\"https:\/\/sites.williams.edu\/mathriddles\/files\/2010\/07\/coins-300x224.jpg\" alt=\"coins\" width=\"300\" height=\"224\" srcset=\"https:\/\/sites.williams.edu\/mathriddles\/files\/2010\/07\/coins-300x224.jpg 300w, https:\/\/sites.williams.edu\/mathriddles\/files\/2010\/07\/coins-401x300.jpg 401w, https:\/\/sites.williams.edu\/mathriddles\/files\/2010\/07\/coins.jpg 500w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>You have 2N coins of varying denominations (each is a non-negative real number) in a line. Players A and B take turns choosing one coin from either end. Prove A always has a strategy that ensures he end up with at least as much as B. Communicated by A. Roy<\/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":[12,13,7],"tags":[20],"class_list":["post-123","post","type-post","status-publish","format-standard","hentry","category-combinatorics","category-games","category-medium","tag-random"],"acf":[],"_links":{"self":[{"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts\/123","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=123"}],"version-history":[{"count":1,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts\/123\/revisions"}],"predecessor-version":[{"id":1164,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts\/123\/revisions\/1164"}],"wp:attachment":[{"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/media?parent=123"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/categories?post=123"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/tags?post=123"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}