There is a 64-square grid (8 x 8 squares). There is a piece that can start in any square. It can only move 3 spaces in a straight line and then move 1 space to the right or the left (the type of L-movement a knight could make on a Chess board but one space farther than a knight before turning). Can this piece end up in a square that is adjacent to its original square?

I think not, but I am not 100% sure. And if it can't, I am having trouble proving this mathematically. Is it just that if it only can move 3 spaces in a straight line, and the board is 8 squares long, you will eventually end up diagonally from the original square?


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The answer is



In one step it always goes to the same color of its originating position. As in checkerboard the adjacent cells have different color then it's impossible.

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