{"id":69,"date":"2010-12-13T16:04:36","date_gmt":"2010-12-13T21:04:36","guid":{"rendered":"http:\/\/puzzlezapper.com\/blog\/2010\/12\/all-pentominoes-in-5\/"},"modified":"2010-12-13T16:02:02","modified_gmt":"2010-12-13T21:02:02","slug":"all-pentominoes-in-5","status":"publish","type":"post","link":"https:\/\/puzzlezapper.com\/blog\/2010\/12\/all-pentominoes-in-5\/","title":{"rendered":"All Pentominoes in 5"},"content":{"rendered":"<p>I&#8217;ve been thinking about variations on the problem of cycling through all twelve pentominoes by moving a single cell at a time. (I wrote about this in a <a href=\"https:\/\/puzzlezapper.com\/blog\/2010\/03\/pentomino-cover-cycles\/\">previous post<\/a>.) Constraining the way that the squares are allowed to move led to something almost like a chess problem.<\/p>\n<div align=\"center\"><img decoding=\"async\" style=\"max-width: 800px;\" src=\"http:\/\/puzzlezapper.com\/aom\/mathrec\/allin5.gif\" \/><\/div>\n<p><b>The problem:<\/b><\/p>\n<p>Starting with the above position, take five turns as follows:<\/p>\n<p>A turn consists of moving one white knight, then moving one black knight, according to standard chess rules.<\/p>\n<p>After each turn, the squares occupied by the ten knights must form two separate pentominoes.<\/p>\n<p>After the fifth turn, all twelve pentominoes must have appeared exactly once. (This includes the two that are present in the starting position.)<\/p>\n[I may make a separate post discussing and spoiling the puzzle later.]\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>I&#8217;ve been thinking about variations on the problem of cycling through all twelve pentominoes by moving a single cell at a time. (I wrote about this in a previous post.) Constraining the way that the squares are allowed to move led to something almost like a chess problem. The problem: Starting with the above position, &hellip; <a href=\"https:\/\/puzzlezapper.com\/blog\/2010\/12\/all-pentominoes-in-5\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">All Pentominoes in 5<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[10,39,11],"class_list":["post-69","post","type-post","status-publish","format-standard","hentry","category-recreational-mathematics","tag-pentominoes","tag-polyform-change-paths","tag-polyominoes"],"_links":{"self":[{"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/posts\/69","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/comments?post=69"}],"version-history":[{"count":1,"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/posts\/69\/revisions"}],"predecessor-version":[{"id":70,"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/posts\/69\/revisions\/70"}],"wp:attachment":[{"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/media?parent=69"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/categories?post=69"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/tags?post=69"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}