ZHED is NP-complete
Computational Complexity
2021-12-16 v1
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.
Cite
@article{arxiv.2112.07914,
title = {ZHED is NP-complete},
author = {Sagnik Saha and Erik D. Demaine},
journal= {arXiv preprint arXiv:2112.07914},
year = {2021}
}