{"id":420,"date":"2013-08-21T16:11:11","date_gmt":"2013-08-21T20:11:11","guid":{"rendered":"https:\/\/jasoncantarella.com\/wordpress\/?p=420"},"modified":"2013-08-21T16:11:26","modified_gmt":"2013-08-21T20:11:26","slug":"solving-mazes-by-coloring","status":"publish","type":"post","link":"https:\/\/jasoncantarella.com\/wordpress\/solving-mazes-by-coloring\/","title":{"rendered":"Solving Mazes by Coloring"},"content":{"rendered":"

Most people know that you can always solve a maze (eventually) by turning left. Here’s a more visual solution to the maze problem which I developed for a elementary school class at Waseca Montessori School in Athens, Georgia. Instead of thinking about the maze, think about the walls of the maze: if there’s a path through, that path has to divide the walls into two disconnected pieces. If you color in the walls differently, the solution to the maze becomes obvious!<\/p>\n

\"16maze_bw\"<\/a> \"16maze_color\"<\/a><\/p>\n

 <\/p>\n

Of course, you can make an even harder maze, with several different solutions, by adding some more connected pieces to the maze (with more colors, of course). Here’s one with 5 components instead of two.<\/p>\n

\"16maze_mc_bw\"<\/a> \"16maze_mc_color\"<\/a><\/p>\n

I made a bunch of mazes with Mathematica for the students to try, which you can print out as PDF files:\u00a0Level 2 Maze<\/a>,\u00a0Level 2 Maze<\/a>,\u00a0Level 3 Maze<\/a>,\u00a0Level 4 Maze<\/a>,\u00a0Level 5 Maze<\/a>,\u00a0Level 6 Maze<\/a>,\u00a0Level 13 Maze<\/a>,\u00a0Level 16 Maze<\/a>.<\/p>\n

You can play with the demonstration by downloading\u00a0Coloring Mazes (CDF)<\/a>\u00a0which is a file in the Wolfram\u00a0Computable Document Format<\/a>, which is really pretty neat! This is now also available as part of the\u00a0Wolfram Demonstrations Project<\/a>.<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Most people know that you can always solve a maze (eventually) by turning left. Here’s a more visual solution to the maze problem which I developed for a elementary school class at Waseca Montessori School in Athens, Georgia. Instead of thinking about the maze, think about the walls of the maze: if there’s a path […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5,6],"tags":[],"class_list":["post-420","post","type-post","status-publish","format-standard","hentry","category-education","category-math"],"_links":{"self":[{"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/posts\/420","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/comments?post=420"}],"version-history":[{"count":2,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/posts\/420\/revisions"}],"predecessor-version":[{"id":426,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/posts\/420\/revisions\/426"}],"wp:attachment":[{"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/media?parent=420"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/categories?post=420"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/tags?post=420"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}