Complexity of Critter Crunch

Abstract

We study the computational complexity of the puzzle game Critter Crunch, where the player has to rearrange Critters on a board in order to eliminate them all. Smaller Critters can be fed to larger Critters, and Critters will explode if they eat too much. Critters come in several different types, sizes, and colors. We prove the NP-hardness of levels that contain Blocker Critters, as well as levels where the player must clear the board in a given number of moves (i.e., “puzzle mode”). We also characterize the complexity of the game, as a function of the number of columns on the board, in two settings: (i) the setting where Critters may have several different colors, but only two possible sizes, and (ii) the setting where Critters come in all three sizes, but with no color variations. In both settings, the game is NP-hard for levels with exactly two columns, and solvable in linear time for levels with only one column or more than two columns.