{"id":474,"date":"2008-06-21T09:54:11","date_gmt":"2008-06-21T13:54:11","guid":{"rendered":"http:\/\/www.shakespeareteacher.com\/blog\/archives\/474"},"modified":"2009-07-28T04:40:02","modified_gmt":"2009-07-28T09:40:02","slug":"conundrum-pic-tac-toe-in-3d-part-iv","status":"publish","type":"post","link":"https:\/\/www.shakespeareteacher.com\/blog\/archives\/474","title":{"rendered":"Conundrum: Pic Tac Toe in 3D, Part IV"},"content":{"rendered":"<p>We haven&#8217;t had one of these in a while&#8230;<\/p>\n<p>In a normal &#8220;Pic Tac Toe&#8221; puzzle, there are nine pictures in a 3&#215;3 grid, like Tic-Tac-Toe. In each of the three rows, three columns, and two diagonals, there is a common theme that unites the three pictures. The challenge is to find the eight themes.<\/p>\n<p>In this &#8220;Pic Tac Toe&#8221; puzzle, however, there are twenty-seven pictures in a 3x3x3 grid, like a Rubik&#8217;s Cube. In each of the nine rows, nine columns, nine pillars, eighteen lateral diagonals, and four cross-cube diagonals, there is a common theme that unites the three pictures. The challenge is to find the forty-nine themes.<\/p>\n<p>Imagine stacking the three levels below on top of one another. For reference, and notation guidelines, check out <a href=\"http:\/\/www.shakespeareteacher.com\/blog\/archives\/388\">my last 3D Pic Tac Toe<\/a>, including the comments. The rules here are identical to that puzzle.<\/p>\n<p>You can click on each image to see a larger version:<\/p>\n<h2>Top Level &#8211; Level A<\/h2>\n<p><a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4A1.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"121\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4A1.jpg\" width=\"150\" \/><\/a><a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4A2.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"150\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4A2.jpg\" width=\"150\" \/><\/a><a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4A3.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"80\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4A3.jpg\" width=\"150\" \/><\/a><br \/>\n<a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4A4.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"200\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4A4.jpg\" width=\"150\" \/><\/a><a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4A5.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"128\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4A5.jpg\" width=\"150\" \/><\/a><a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4A6.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"210\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4A6.jpg\" width=\"150\" \/><\/a><br \/>\n<a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4A7.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"193\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4A7.jpg\" width=\"150\" \/><\/a><a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4A8.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"115\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4A8.jpg\" width=\"150\" \/><\/a><a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4A9.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"103\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4A9.jpg\" width=\"150\" \/><\/a><\/p>\n<h2>Middle Level &#8211; Level B<\/h2>\n<p><a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4B1.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"105\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4B1.jpg\" width=\"150\" \/><\/a><a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4B2.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"128\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4B2.jpg\" width=\"150\" \/><\/a><a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4B3.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"262\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4B3.jpg\" width=\"150\" \/><\/a><br \/>\n<a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4B4.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"201\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4B4.jpg\" width=\"150\" \/><\/a><a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4B5.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"202\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4B5.jpg\" width=\"150\" \/><\/a><a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4B6.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"220\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4B6.jpg\" width=\"150\" \/><\/a><br \/>\n<a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4B7.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"153\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4B7.jpg\" width=\"150\" \/><\/a><a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4B8.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"84\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4B8.jpg\" width=\"150\" \/><\/a><a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4B9.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"167\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4B9.jpg\" width=\"150\" \/><\/a><\/p>\n<h2>Bottom Level &#8211; Level C<\/h2>\n<p><a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4C1.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"201\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4C1.jpg\" width=\"150\" \/><\/a><a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4C2.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"126\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4C2.jpg\" width=\"150\" \/><\/a><a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4C3.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"112\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4C3.jpg\" width=\"150\" \/><\/a><br \/>\n<a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4C4.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"185\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4C4.jpg\" width=\"150\" \/><\/a><a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4C5.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"159\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4C5.jpg\" width=\"150\" \/><\/a><a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4C6.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"234\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4C6.jpg\" width=\"150\" \/><\/a><br \/>\n<a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4C7.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"213\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4C7.jpg\" width=\"150\" \/><\/a><a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4C8.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"150\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4C8.jpg\" width=\"150\" \/><\/a><a href=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4C9.jpg\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" height=\"84\" src=\"http:\/\/www.shakespeareteacher.com\/blog\/wp-content\/images\/P4C9.jpg\" width=\"150\" \/><\/a><\/p>\n<p>Please post whatever you come up with in the comments section.<\/p>\n<p>Enjoy!<\/p>\n<p>UPDATE: Correct themes provided by Benjamin Baxter (3), Billie (24), and Neel Mehta (16). Alternate themes suggested by Benjamin Baxter (1), Billie (2), and Neel Mehta (5). See comments for discussion, or click <a href=http:\/\/www.shakespeareteacher.com\/blog\/archives\/474#comment-85996>here<\/a> to skip right to the answers.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We haven&#8217;t had one of these in a while&#8230; In a normal &#8220;Pic Tac Toe&#8221; puzzle, there are nine pictures in a 3&#215;3 grid, like Tic-Tac-Toe. In each of the three rows, three columns, and two diagonals, there is a common theme that unites the three pictures. The challenge is to find the eight themes. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[30,54,53,26],"tags":[],"class_list":["post-474","post","type-post","status-publish","format-standard","hentry","category-conundrum","category-pic-tac-toe","category-special-feature","category-visual-arts"],"_links":{"self":[{"href":"https:\/\/www.shakespeareteacher.com\/blog\/wp-json\/wp\/v2\/posts\/474","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.shakespeareteacher.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.shakespeareteacher.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.shakespeareteacher.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.shakespeareteacher.com\/blog\/wp-json\/wp\/v2\/comments?post=474"}],"version-history":[{"count":1,"href":"https:\/\/www.shakespeareteacher.com\/blog\/wp-json\/wp\/v2\/posts\/474\/revisions"}],"predecessor-version":[{"id":1591,"href":"https:\/\/www.shakespeareteacher.com\/blog\/wp-json\/wp\/v2\/posts\/474\/revisions\/1591"}],"wp:attachment":[{"href":"https:\/\/www.shakespeareteacher.com\/blog\/wp-json\/wp\/v2\/media?parent=474"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shakespeareteacher.com\/blog\/wp-json\/wp\/v2\/categories?post=474"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shakespeareteacher.com\/blog\/wp-json\/wp\/v2\/tags?post=474"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}