TL;DR
This paper proves that determining the solvability of Solitaire Chess, a single-player chess puzzle, is an NP-complete problem, highlighting its computational complexity.
Contribution
It establishes the NP-completeness of Solitaire Chess, a novel complexity result for a popular logic puzzle.
Findings
Solitaire Chess is NP-complete.
Deciding solvability is computationally hard.
The problem is as hard as other NP-complete problems.
Abstract
"Solitaire Chess" is a logic puzzle published by Thinkfun, that can be seen as a single person version of traditional chess. Given a chess board with some chess pieces of the same color placed on it, the task is to capture all pieces but one using only moves that are allowed in chess. Moreover, in each move one piece has to be captured. We prove that deciding if a given instance of Solitaire Chess is solvable is NP-complete.
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Taxonomy
TopicsArtificial Intelligence in Games · Teaching and Learning Programming · Computability, Logic, AI Algorithms