tag:blogger.com,1999:blog-264226589944705290.post7713475918331386887..comments2023-09-26T02:41:59.382-07:00Comments on God Plays Dice: Best Wikipedia article title everMichael Lugohttp://www.blogger.com/profile/15671307315028242949noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-264226589944705290.post-23737308844601910512008-09-07T12:38:00.000-07:002008-09-07T12:38:00.000-07:00Yes any 2 different colored squares remove will yi...Yes any 2 different colored squares remove will yield a tileable board. <BR/><BR/>Draw any "path" that goes through all squares exactly once and finishing the same square you began. <BR/><BR/>The path gives a way to tile the board (actually 2 ways) by always placing dominoes on the path direction (that is, each ominio covering 2 adjacent squares on the path).<BR/><BR/>Remove 2 different colored squares. <BR/>That splits the path in 2 disjoint subpaths, each one having an even length (this is where diff colors matter).<BR/><BR/>Retile the 2 subpaths with the same method and violá! you've tile the mutilated boarddrinihttps://www.blogger.com/profile/06533961354442533309noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-77178650349290818652008-09-07T08:48:00.000-07:002008-09-07T08:48:00.000-07:00OOppsy7, it's not necessarily that intuitive. You...OOppsy7, it's not necessarily that intuitive. You can't place your dominoes willy-nilly and expect to cover the whole board, no matter what its shape. There's still more work to do.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-31079214660220061882008-09-07T05:57:00.000-07:002008-09-07T05:57:00.000-07:00Color squares black and white in the usual way. It...Color squares black and white in the usual way. It is easy to see that if two squares of the same color are removed, then tiling is impossible. Is a tiling always possible if two squares of different colors are removed?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-88126125942504833612008-09-07T02:16:00.000-07:002008-09-07T02:16:00.000-07:00The chessboard is made of black and white squares,...The chessboard is made of black and white squares, where no single color is side by side. Make your domino half black, half white. The rest is intuitive.Anonymoushttps://www.blogger.com/profile/16343730322759854973noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-16097813643937056712008-09-05T08:45:00.000-07:002008-09-05T08:45:00.000-07:00I've seen this problem before and I know the solut...I've seen this problem before and I know the solution to the original problem, but I'm not quite sure about the other two (the general rules). I hope I've got it, at least the obvious choice, but I'm racking my brain to be sure it's possible. Ha....maybe I'll give that original problem to my 7th-Graders some day when they finish a quiz. That ought to keep them busy for quite a whileSean Hendersonhttps://www.blogger.com/profile/00996947122054737906noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-70272161762860522522008-09-05T08:42:00.000-07:002008-09-05T08:42:00.000-07:00This comment has been removed by the author.Sean Hendersonhttps://www.blogger.com/profile/00996947122054737906noreply@blogger.com