{"id":112,"date":"2009-06-02T00:49:22","date_gmt":"2009-06-02T07:49:22","guid":{"rendered":"http:\/\/new-gro.dyn.hhhh.org\/joeboy\/blog\/?p=112"},"modified":"2014-07-22T16:31:29","modified_gmt":"2014-07-22T23:31:29","slug":"find-five-rectangles-that-tile-a-square","status":"publish","type":"post","link":"https:\/\/www.hhhh.org\/joeboy\/blog\/?p=112","title":{"rendered":"Find five rectangles that tile a square"},"content":{"rendered":"<p>This problem is representative of a class of problems that I can solve &#8211; but only thought brute force. In some cases &#8211; like this one &#8211; I can winnow my guessing spaces though the use of logic and\u00a0algebra\u00a0&#8211; but it is still a brute force attack. What I don&#8217;t see is how to make a non-brute force algorithmic attack on this problem.<\/p>\n<p>This problem was phrased with five rectangles tiled to cover a square &#8211; with a much larger number of squares I could not easily do it by hand and if I was to write a program to do it that attack would also be brute force.\u00a0<\/p>\n<p>Ugly as it is &#8211; here is how I solved this problem.\u00a0<\/p>\n<figure id=\"attachment_113\" aria-describedby=\"caption-attachment-113\" style=\"width: 568px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-113    \" title=\"five_rectangles_tileing_a_square\" src=\"https:\/\/www.hhhh.org\/joeboy\/blog\/wp-content\/uploads\/2009\/06\/five_rectangles_tileing_a_square.jpg\" alt=\"Find five rectangles with sides of length (1..10) that tile a square\" width=\"568\" height=\"765\" \/><figcaption id=\"caption-attachment-113\" class=\"wp-caption-text\">Find five rectangles with sides of length (1..10) that tile a square<\/figcaption><\/figure>\n<p>I just looked at the Mathproblems.info site where I saw this problem and they show three more solutions. One more with side length of 13 and two more with side length of 11. I was less thorough with my search of the 11 options and stopped on 13 after I found the first solution but the techniques seem to be the same for all solutions. Still brute force-ish though. There must be a better way to formalize solving this type of problem.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This problem is representative of a class of problems that I can solve &#8211; but only thought brute force. In some cases &#8211; like this one &#8211; I can winnow my guessing spaces though the use of logic and\u00a0algebra\u00a0&#8211; but it is still a brute force attack. What I don&#8217;t see is how to make [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13,9,12],"tags":[],"class_list":["post-112","post","type-post","status-publish","format-standard","hentry","category-algerbra","category-math","category-problems"],"_links":{"self":[{"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=\/wp\/v2\/posts\/112","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=112"}],"version-history":[{"count":8,"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=\/wp\/v2\/posts\/112\/revisions"}],"predecessor-version":[{"id":116,"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=\/wp\/v2\/posts\/112\/revisions\/116"}],"wp:attachment":[{"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=112"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=112"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=112"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}