Mastermind is NP-Complete

Jeff Stuckman; Guo-Qiang Zhang

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Mastermind is NP-Complete

Jeff Stuckman·Guo-Qiang Zhang

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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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Jeff Stuckman, Guo-Qiang Zhang. 2005-12-13. Mastermind is NP-Complete. https://arxiv.org/abs/cs/0512049

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