{"id":10831,"date":"2015-03-14T11:15:35","date_gmt":"2015-03-14T15:15:35","guid":{"rendered":"http:\/\/mjtsai.com\/blog\/?p=10831"},"modified":"2024-01-15T14:14:14","modified_gmt":"2024-01-15T19:14:14","slug":"simple-proof-of-the-tetris-lamp","status":"publish","type":"post","link":"https:\/\/mjtsai.com\/blog\/2015\/03\/14\/simple-proof-of-the-tetris-lamp\/","title":{"rendered":"Simple Proof of the Tetris Lamp"},"content":{"rendered":"<a href=\"http:\/\/jackm.co.uk\/posts\/2015\/01\/11\/the-simple-proof-of-the-tetris-lamp\/\">Jack Morris<\/a> (via <a href=\"https:\/\/news.ycombinator.com\/item?id=8870479\">Hacker News<\/a>):\n<blockquote cite=\"http:\/\/jackm.co.uk\/posts\/2015\/01\/11\/the-simple-proof-of-the-tetris-lamp\/\">The lamp itself is composed of 7 individual pieces, containing a total of 28 squares. Therefore, assuming we can indeed form it into a rectangle, it would have to be 7x4 or 14x2 squares in size. I\u2019m using the former case here simply because it\u2019s a more natural shape, however this proof applies equally as well to the latter. Now imagine that we label each of these squares with a colour - either black or white - such that they form a checkerboard pattern as shown above. Notice that the number of black squares <strong>must<\/strong> be equal to the number of white, a property we\u2019ll exploit.\n\nSo that\u2019s 14 black squares, and 14 white. Looking at each of the pieces individually, the issue with our assumption quickly appears.<\/blockquote>","protected":false},"excerpt":{"rendered":"<p>Jack Morris (via Hacker News): The lamp itself is composed of 7 individual pieces, containing a total of 28 squares. Therefore, assuming we can indeed form it into a rectangle, it would have to be 7x4 or 14x2 squares in size. I\u2019m using the former case here simply because it\u2019s a more natural shape, however [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"apple_news_api_created_at":"2024-01-15T19:13:54Z","apple_news_api_id":"dd6cb8ea-3686-4a2b-96d6-52bfbcffb943","apple_news_api_modified_at":"2024-01-15T19:13:54Z","apple_news_api_revision":"AAAAAAAAAAD\/\/\/\/\/\/\/\/\/\/w==","apple_news_api_share_url":"https:\/\/apple.news\/A3Wy46jaGSiuW1lK_vP-5Qw","apple_news_coverimage":0,"apple_news_coverimage_caption":"","apple_news_is_hidden":false,"apple_news_is_paid":false,"apple_news_is_preview":false,"apple_news_is_sponsored":false,"apple_news_maturity_rating":"","apple_news_metadata":"\"\"","apple_news_pullquote":"","apple_news_pullquote_position":"","apple_news_slug":"","apple_news_sections":"\"\"","apple_news_suppress_video_url":false,"apple_news_use_image_component":false,"footnotes":""},"categories":[2],"tags":[259,1662],"class_list":["post-10831","post","type-post","status-publish","format-standard","hentry","category-technology","tag-math","tag-tetris"],"apple_news_notices":[],"_links":{"self":[{"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/posts\/10831","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/comments?post=10831"}],"version-history":[{"count":2,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/posts\/10831\/revisions"}],"predecessor-version":[{"id":41770,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/posts\/10831\/revisions\/41770"}],"wp:attachment":[{"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/media?parent=10831"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/categories?post=10831"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/tags?post=10831"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}