Is it possible to tile a 10×10 chessboard with (non-overlapping) T-tetrominos?
If so, how? If not, prove it's impossible.
Bonus: Which Tetris pieces can used to tile a 10×10 board, allowing reflections?
It is certainly posssible to tile a regular 8×8 chessboard. Below is a failed attempt to extend that tiling to a 10×10 board, which misses some squares in the upper left and lower right. The colors don't matter, they're just there to make the picture more clear.
Answer
It is not possible. The area of a 10×10 checkerboard is 100, so it takes 25 T pieces to have the same area. The checkerboard has the same number of red and black squares, but each piece covers three of one color and one of the other. 25 pieces cannot cover 50 squares of each color, the most even they can get is 51−49
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