Imagine a football game played on a six-by-six grid in which a very fast runner starts on the north side of the grid and tries to maneuver past three tackles from the opposite team. Under the rules of this game, the runner's freedom of motion is constricted: he can move only to one of the three grid spaces that are south, southeast or southwest of the space on which he begins. Because he is so fast, however, the runner can make two moves in each turn. The slower tackles can make only one move per turn, but each can move to any adjacent grid space (or simply stay put) [see illustration A].
The runner wins the game if he reaches the southernmost row of grid spaces. The tackles win if they block the runner by occupying all the spaces in front of him (the spaces to the south, southeast and southwest). Suppose the runner can begin in any grid space in the northernmost row. After observing the runner's starting point, the three tackles can place themselves in any grid space that is at least three spaces away from the runner. Illustration B shows one possible initial configuration. The runner goes first, making two moves, and then each of the tackles makes one move, and so on. Can either the runner or the tackles guarantee a win? And if so, how?
This article was originally published with the title Defense in Depth.