Demaine Eric D., Demaine Martin L., Verril Helena A. Coin-Moving Puzzles

MSRI Publications Volume 42, 2002. — 27 p.This is a new family of one-player games, involving the movement of coins from one con guration 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 nding a solution.