{"id":824,"date":"2013-12-18T16:48:48","date_gmt":"2013-12-18T16:48:48","guid":{"rendered":"http:\/\/mathriddles.williams.edu\/?p=824"},"modified":"2025-01-27T09:41:31","modified_gmt":"2025-01-27T14:41:31","slug":"we-value-your-input-2","status":"publish","type":"post","link":"https:\/\/sites.williams.edu\/mathriddles\/articles\/we-value-your-input-2\/","title":{"rendered":"We Value Your Input (NEW: Posted December 18, 2013)"},"content":{"rendered":"<p>Alice and Bob are playing the following game: Alice has a secret polynomial\u00a0P(x) = a_0 + a_1 x + a_2 x^2 + \u2026 + a_n x^n, with non-negative integer\u00a0coefficients a_0, a_1, \u2026, a_n. At each turn, Bob picks an integer k and\u00a0Alice tells Bob the value of P(k). Find, as a function of the degree n, the\u00a0minimum number of turns Bob needs to completely determine Alice\u2019s\u00a0polynomial P(x).\u00a0<em>Hint: the answer is much smaller than you might believe!<\/em><\/p>\n<p>Note: This problem was the October Conundrum challenge at Williams College. Communicated by Michael Biro.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Alice and Bob are playing the following game: Alice has a secret polynomial\u00a0P(x) = a_0 + a_1 x + a_2 x^2 + \u2026 + a_n x^n, with non-negative integer\u00a0coefficients a_0, a_1, \u2026, a_n. At each turn, Bob picks an integer k and\u00a0Alice tells Bob the value of P(k). Find, as a function of the degree&hellip;<\/p>\n","protected":false},"author":2861,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[2,6,8,18],"tags":[],"class_list":["post-824","post","type-post","status-publish","format-standard","hentry","category-articles","category-hard","category-new-riddles","category-number-theory"],"acf":[],"_links":{"self":[{"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts\/824","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=824"}],"version-history":[{"count":1,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts\/824\/revisions"}],"predecessor-version":[{"id":1123,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts\/824\/revisions\/1123"}],"wp:attachment":[{"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/media?parent=824"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/categories?post=824"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/tags?post=824"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}