The "Game about Squares" is NP-hard

TL;DR

This paper proves that determining whether all squares can be moved onto their target dots in the 'Game about Squares' is an NP-hard problem, highlighting its computational complexity.

Contribution

It establishes the NP-hardness of the decision problem in the 'Game about Squares,' a previously unclassified puzzle, through formal computational complexity analysis.

Findings

The problem is NP-hard.

Moving all squares onto their dots is computationally difficult.

The game has inherent complexity similar to other NP-hard puzzles.

Abstract

In the "Game about Squares" the task is to push unit squares on an integer lattice onto corresponding dots. A square can only be moved into one given direction. When a square is pushed onto a lattice point with an arrow the direction of the square adopts the direction of the arrow. Moreover, squares can push other squares. In this paper we study the decision problem, whether all squares can be moved onto their corresponding dots by a finite number of pushes. We prove that this problem is NP-hard.