The Hardness of the Lemmings Game, or "Oh no, more NP-Completeness Proofs"

Abstract

In the computer game ‘Lemmings’, the player must guide a tribe of green-haired lemming creatures to safety, and save them from an untimely demise. We formulate the decision problem which is, given a level of the game, to decide whether it is possible to complete the level (and hence to find a solution to that level). Under certain limitations, this can be decided in polynomial time, but in general the problem is shown to be NP-Hard. This can hold even if there is only a single lemming to save, thus showing that it is hard to approximate the number of saved lemmings to any factor. 1