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Terrific reasoning! That same "checkerboard coloring" strategy is used a lot for figuring out tiling problems. It is too bad the lamp wasn't made of pentominoe
by jones1618 12y ago
Terrific reasoning! That same "checkerboard coloring" strategy is used a lot for figuring out tiling problems.
It is too bad the lamp wasn't made of pentominoes (the 12 Tetris-like pieces with 5 squares vs. your tetrominoes with 4 squares.). See http://en.wikipedia.org/wiki/Pentomino http://en.wikipedia.org/wiki/Pentomino. There are 2339 ways to form these into a perfect 6x10 rectangle (more if you include rotations and reflections).
FYI: The creator of Tetris actually got the idea for his game pieces from Solomon W. Golomb's book "Polyominoes" that introduced all kinds of variations on tiling puzzles and proofs. Chapter one starts using checkerboard reasoning right off the bat. So, you are in good company.