{"id":126,"date":"2010-07-13T18:58:34","date_gmt":"2010-07-13T18:58:34","guid":{"rendered":"http:\/\/mathriddles.williams.edu\/?p=126"},"modified":"2025-01-27T09:41:32","modified_gmt":"2025-01-27T14:41:32","slug":"tiling-rectangular-boxes","status":"publish","type":"post","link":"https:\/\/sites.williams.edu\/mathriddles\/difficulty\/hard\/tiling-rectangular-boxes\/","title":{"rendered":"Tiling Rectangular Boxes"},"content":{"rendered":"<p>For each positive integer n, consider a 2 by n rectangle. It can be tiled with n blocks, where each block is 1 by 2. How many different ways can it be tiled? What if instead of a 2 by n rectangle we were to consider a 3 by n rectangle (where now of course n would have to be an even integer). How many ways could this be tiled with 1 by 2 blocks?<\/p>\n<p>Note the blocks look like [][], and can be oriented either horizontally or vertically.<\/p>\n<p>Communicated by A. Kanevsky.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>For each positive integer n, consider a 2 by n rectangle. It can be tiled with n blocks, where each block is 1 by 2. How many different ways can it be tiled? What if instead of a 2 by n rectangle we were to consider a 3 by n rectangle (where now of course&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],"tags":[],"class_list":["post-126","post","type-post","status-publish","format-standard","hentry","category-combinatorics","category-hard"],"acf":[],"_links":{"self":[{"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts\/126","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=126"}],"version-history":[{"count":1,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts\/126\/revisions"}],"predecessor-version":[{"id":1163,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts\/126\/revisions\/1163"}],"wp:attachment":[{"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/media?parent=126"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/categories?post=126"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/tags?post=126"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}