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.