One knight game
In the one knight game, there is only one knight on the chessboard. Somebody loses when a knight has no more unoccupied spaces to go. When a space is "occupied" it means that the knight has been there before. If two players are playing this game and play optimally and the starting position is the one below, then who will win?
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1 solution
It will help to first simplify the game. Imagine if it was only a 4 by 2 board, then there would only be one move to make, right? Then the player who goes first wins.
How about a 8 by 8 chessboard? The answer is surprisingly simple. Divide the board into 8 equal pieces, or 4 by 2 rectangles and it should fill up the whole board. So just picture that and always move in the other square that is in the 4 by 2 rectangle. The other player can't do any thing because after that move, they should always have to move to another 4 by 2 square, then repeat the process.