* Jason <jason@lunkwill.org> [Mar 31. 2013 09:21]:
This blog is thoroughly delightful, with brain teasers and historical oddities. In particular, I thought the solution to this tiling problem was quite lovely, and generalizes to other shapes:
http://www.futilitycloset.com/2012/09/30/tiling-task/
Upon further reading, it appears to be related to the mutilated chessboard problem.
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That's a mild generalization of the problem whether a chessboard with two opposing corners removed can be covered with dominoes. (Dunno whether this is just the "mutilated chessboard problem"). Here's one that I find delightful: Show that for every possible coloring of the plane with two colors there exist, for every distance d, two points of distance d with the same color. [Spoiler below] ... ... ... soon be spoiler ... ... ... oh noes! ... Spoiler: Put an equilateral triangle with side length d anywhere. At least two vertices must have the same color. Is this neat or just dumb? Discuss with your neighbor.