tag:blogger.com,1999:blog-30937878.post194765869933759932..comments2023-06-21T04:24:54.427-04:00Comments on Graph Theory: Tiling chessboard by L-shaped trominoesShiva Kintalihttp://www.blogger.com/profile/07853545928906483737noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-30937878.post-69158667714829496652008-05-28T17:15:00.000-04:002008-05-28T17:15:00.000-04:00L as in:XXXor as in:XXXX?I assume the first, since...L as in:<BR/>X<BR/>XX<BR/><BR/>or as in:<BR/>X<BR/>X<BR/>XX<BR/>?<BR/><BR/>I assume the first, since there is no way to cover a 2x2 board with the second + 1. If so, I know an inductive solution. The question is:<BR/>Can you fill all but one cube of a (2^n)^3 cube grid with 7/8 cubes filled 2x2x2 pieces? (i. e. remove a single cube from a 2x2x2 cube piece to make a 7/8) Can you place the missing cube anywhere you want in the cube grid?<BR/><BR/>I'm sure if you can do the 2d solution you can do the 3d, but it's another way to think of it, at least.Anonymousnoreply@blogger.com