Two knights (black and white, the latter going first) start on opposing corners of a chessboard, moving across it in the usual manner, attempting to capture each other: the knight who first lands on the square currently occupied by the other knight (i.e. capturing it) wins.
To ensure that the game doesn't go on forever, each knight must increase the distance from his point of origin (unless that move would immediately capture the other knight). If neither can move forward nor capture the other then they are tied.
Show whether one of the knights can force a win, tie or loss.
There are six cases to consider: whether either of them can force a win, tie or loss.
Each move sends them to a square of a different color. A knight must start from a different-colored square to end up on the square the other knight is on. Since both start in opposing corners they start on squares of the same color. Therefore white (going first) can never win and black never lose.
Black can force a win if and only if white cannot force a tie. White can force a loss if and only if black cannot force a tie. Hence it suffices to show 1. either that black can win or white can tie and 2. either that white can lose or black can tie.