Snake-in-the-box

Statement

The snake-in-the-box problem in graph theory and coding theory deals with finding a certain kind of path along the edges of a hypercube. This path starts at one corner and travels along the edges to as many corners as it can reach. After it gets to a new corner, the previous corner and all of its neighbors must be marked as unusable. The path must never travel to a corner which has been marked unusable.