ZHED is NP-complete

12/15/2021

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by   Sagnik Saha, et al.

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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.