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Source: Futility Closet
Each square on a chessboard contains an arrow point up, down, left or right. You start in the bottom left square. Every second you move one square in the direction shown by the arrow in your square. Just after you move, the arrow on the square you moved from rotates 90° clockwise. If an arrow would take you off the edge of the board, you stay in that square (the arrow will still rotate).
You win the game if you reach the top right square of the chessboard. Can I design a starting arrangement of arrows that will prevent you from winning?
It was once claimed that there are 204 squares on a chessboard. Can you justify this claim?