NP-Hardness of a 2D, a 2.5D, and a 3D Puzzle Game

TL;DR

This paper proves that three popular puzzle video games—Baba Is You, Fez, and Catherine—are NP-hard, demonstrating their computational complexity through simple reductions.

Contribution

It provides the first NP-hardness proofs for these three distinct puzzle games, highlighting their computational difficulty.

Findings

Baba Is You is NP-hard due to its rule-rewriting mechanics.

Fez's view-swapping mechanic leads to NP-hardness.

Catherine's 3D block rearrangement is NP-hard.

Abstract

In this paper, we give simple NP-hardness reductions for three popular video games. The first is Baba Is You, an award winning 2D block puzzle game with the key premise being the ability to rewrite the rules of the game. The second is Fez, a puzzle platformer whose main draw is the ability to swap between four different 2-dimensional views of the player's position. The final is Catherine, a 3-dimensional puzzle game where the player must climb a tower of rearrangeable blocks.