ZHED is NP-complete

TL;DR

This paper proves that the puzzle game ZHED, even with only 1 tiles, is NP-complete by reducing from rectilinear planar monotone 3SAT, establishing its computational complexity.

Contribution

It demonstrates the NP-completeness of ZHED with minimal tiles, expanding understanding of its computational difficulty.

Findings

ZHED is NP-complete with 1 tiles

NP-completeness proven via reduction from rectilinear planar monotone 3SAT

Complexity holds even with minimal game components

Abstract

We prove that the 2017 puzzle game ZHED is NP-complete, even with just 1 tiles. Such a puzzle is defined by a set of unit-square 1 tiles in a square grid, and a target square of the grid. A move consists of selecting an unselected 1 tile and then filling the next unfilled square in a chosen direction from that tile (similar to Tipover and Cross Purposes). We prove NP-completeness of deciding whether the target square can be filled, by a reduction from rectilinear planar monotone 3SAT.