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Riddle: Tiling Without Corners

You can easily "tile" an 8x8 chessboard with 32 2x1 tiles, meaning that you can place these 32 tiles on the board and cover every square.

But if you take away two opposite corners from the chessboard, it becomes impossible to tile this new 62-square board.

Can you explain why tiling this board isn't possible?

Try coloring the board like a chessboard is colored, and see if that gives you any ideas.

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