How to cover 9 x 10 chessboard with Tetris pieces
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1. Prove or disprove: is it possible to tile a 9 x 10 chessboard with Tetris pieces?
2. Is it possible to perfectly tile a 4 x 7 chessboard with the 7 Tetris pieces?
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Solution Summary
The area of the chessboard is 90. One Tetris is made of four squares, so it has area of 4. To cover the chessboard with Tetris pieces, 90 must be evenly divided by 4.
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1. Prove or disprove: is it possible to tile a 9 x 10 chessboard with Tetris pieces?
Answer: It is impossible.
The area of the chessboard is 90. One Tetris is made of four squares, so it has area of 4. To cover the chessboard with Tetris pieces, 90 must be evenly divided by 4.
Since 90 is not divisible by 4, we conclude that it is impossible to tile a 9 x 10 chessboard with Tetris pieces.
2. Is it possible to perfectly tile a 4 x 7 chessboard with the 7 Tetris pieces?
This problem is harder. We will start with counting the 7-Tetris pieces from 1 to 7:
1 2 3 4 ...
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