Subway Shuffle is PSPACE-complete

Abstract: Subway shuffle is an addicting puzzle game created by Bob Hearn. It is played on a graph with colored edges that represent subway lines; colored tokens that represent subway cars are placed on the nodes of the graph. A token can be moved from its current node to an empty one, but only if the two nodes are connected with an edge of the same color of the token. The aim of the game is to move a special token to its final target position. We prove that deciding if the game has a solution is PSPACE-complete even when the game graph is planar.

Subway Shuffle Level 14

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