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It is a 'tassellation' or 'tiling' problem. Specifically it is a
'counting problem': It asks to count the number of ways in which you can cover up a given rectangular grid using only a specific tile (the
letter 'L' ). Tiling problems are quite well known: for example the following
link deals with tiling a rectangular board using Ls and squares
(similar to this problem but a bit more general):
https://cs.uwaterloo.ca/journals/JIS/VOL10/Heubach/heubach40.pdf
Since the problem at hand deals with a 2x3 L, which is a special case of
tetromino (a L-tetromino), you may also find some useful hints by
searching the web for tiling with tetrominos, for
ex. http://math.stackexchange.com/questions/513227/an-olympiad-problem-tiling-a-rectangle-with-the-l-tetromino
good luck!
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Brick Tiling
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It is a 'tassellation' or 'tiling' problem. Specifically it is a 'counting problem': It asks to count the number of ways in which you can cover up a given rectangular grid using only a specific tile (the letter 'L' ). Tiling problems are quite well known: for example the following link deals with tiling a rectangular board using Ls and squares (similar to this problem but a bit more general): https://cs.uwaterloo.ca/journals/JIS/VOL10/Heubach/heubach40.pdf Since the problem at hand deals with a 2x3 L, which is a special case of tetromino (a L-tetromino), you may also find some useful hints by searching the web for tiling with tetrominos, for ex. http://math.stackexchange.com/questions/513227/an-olympiad-problem-tiling-a-rectangle-with-the-l-tetromino
good luck!