One Hex reduction to rule them all: Quoridor, Maze Attack, Pinko Pallino and Blockade are PSPACE-complete

Francesco Carboni; Daniele Muscillo

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arXiv · 2606.28931

One Hex reduction to rule them all: Quoridor, Maze Attack, Pinko Pallino and Blockade are PSPACE-complete

Francesco Carboni·Daniele Muscillo

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Abstract

Quoridor is a popular award-winning board game whose computational complexity, listed among the open problems of the Demaine-Hearn survey, remained open for nearly two decades. It was settled only recently, via a reduction from the formula game $G_{pos}$ tailored to Quoridor. We give a shorter and more general proof: a single reduction from Reisch's planar graph-Hex, in which wall placement encodes the path-connection structure of Hex. The same construction settles three closely related games -- Maze Attack and Pinko Pallino with no change, and Blockade with only minor adaptations -- showing that all four are PSPACE-complete, the latter three for the first time. More generally, our reduction shows that any race-and-wall game is PSPACE-complete.

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Francesco Carboni, Daniele Muscillo. 2026-06-27. One Hex reduction to rule them all: Quoridor, Maze Attack, Pinko Pallino and Blockade are PSPACE-complete. https://arxiv.org/abs/2606.28931

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