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Can you cover a 9x9 square chessboard with 1x2 dominos?

Can you cover an 8x8 square chessboard with 1x2 dominos?
Can you cover an 8x8 square chessboard with the top-left and bottom-right corners removed with 1x2 dominos?

User Jenk
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Final answer:

Yes, you can cover a chessboard with 1x2 dominos. A 9x9 chessboard would require 41 dominos, while an 8x8 chessboard would require 32 dominos. Removing the top-left and bottom-right corners from an 8x8 chessboard would require 30 dominos.

Step-by-step explanation:

Yes, you can cover a 9x9 square chessboard with 1x2 dominos. To do this, imagine the chessboard as a grid of 1x1 squares. Each 1x2 domino covers two of these squares. Since the chessboard has a total of 81 squares (9x9), and each domino covers two squares, you would need 40.5 dominos to completely cover the chessboard. Since you cannot have half a domino, you would use 41 dominos to cover the board.

Similarly, you can cover an 8x8 square chessboard with 1x2 dominos. The chessboard has a total of 64 squares (8x8), and each domino covers two squares. Therefore, you would need 32 dominos to completely cover the chessboard.

If you remove the top-left and bottom-right corners from an 8x8 square chessboard, you will be left with 60 squares. Since each domino covers two squares, you would need 30 dominos to cover this modified chessboard.

User Andez
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