We prove that a variant of 2048, a popular online puzzle game, is PSPACE-Complete. Our hardness result holds for a version of the problem where the player has oracle access to the computer player's moves. Specifically, we show that for an n × n game board G, computing a sequence of moves to reach a particular configuration C from an initial configuration C 0 is PSPACE-Complete. Our reduction is from Nondeterministic Constraint Logic (NCL). We also show that determining whether or not there exists a fixed sequence of moves S ∈ {⇑ , ⇓, ⇐, ⇒} k of length k that results in a winning configuration for an n × n game board is fixedparameter tractable (FPT). We describe an algorithm to solve this problem in O(4 k n 2 ) time.
Mehta proved that the n × n version of the game 2048 is PSPACE hard REF assuming that the random moves are known in advance.
2048 is (PSPACE) Hard, but Sometimes Easy
ArXiv
ArXiv
Computer Science Mathematics