We introduce a new family of one-player games, involving the movement of coins from one configuration to another. Moves are restricted so that a coin can be placed only in a position that is adjacent to at least two other coins. The goal of this paper is to specify exactly which of these games are solvable. By introducing the notion of a constant number of extra coins, we give tight theorems characterizing solvable puzzles on the square grid and equilateral-triangle grid. These existence results are supplemented by polynomial-time algorithms for finding a solution.
- Pub Date:
- March 2002
- Computer Science - Discrete Mathematics;
- Computer Science - Computational Geometry;
- Computer Science - Computer Science and Game Theory;
- 25 pages, 33 figures. To appear in the book More Games of No Chance edited by Richard Nowakowski and published by MSRI