Mastermind is NP-Complete
Jeff Stuckman, Guo-Qiang Zhang
TL;DR
This paper proves that the Mastermind Satisfiability Problem is NP-complete, highlighting its computational complexity and connecting it to other well-known puzzles like Minesweeper and the 15-puzzle.
Contribution
It establishes the NP-completeness of MSP, providing new insights into its computational difficulty and its relation to other classic puzzles.
Findings
MSP is NP-complete
Highlights computational challenge of Mastermind
Connects MSP to other NP-complete puzzles
Abstract
In this paper we show that the Mastermind Satisfiability Problem (MSP) is NP-complete. The Mastermind is a popular game which can be turned into a logical puzzle called Mastermind Satisfiability Problem in a similar spirit to the Minesweeper puzzle. By proving that MSP is NP-complete, we reveal its intrinsic computational property that makes it challenging and interesting. This serves as an addition to our knowledge about a host of other puzzles, such as Minesweeper, Mah-Jongg, and the 15-puzzle.
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Taxonomy
TopicsArtificial Intelligence in Games · Algorithms and Data Compression · Computability, Logic, AI Algorithms