# Mastermind is NP-Complete

• Published in 2005
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.

## Other information

key
Stuckman2005
type
article
2012-09-02
date_published
2005-12-01
arxivId
cs/0512049
journal
Arxiv preprint cs/0512049
keywords
computational complexity,mastermind,theory of computation
pages
1--7

### BibTeX entry

@article{Stuckman2005,
key = {Stuckman2005},
type = {article},
title = {Mastermind is NP-Complete},
author = {Stuckman, Jeff and Zhang, Guo-Qiang},
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.},
comment = {},
date_published = {2005-12-01},
urls = {http://arxiv.org/abs/cs/0512049,http://arxiv.org/pdf/cs/0512049v1},
collections = {Puzzles,Basically computer science,Games to play with friends,Computational complexity of games},
archivePrefix = {arXiv},
arxivId = {cs/0512049},
eprint = {cs/0512049},
journal = {Arxiv preprint cs/0512049},
keywords = {computational complexity,mastermind,theory of computation},
month = {dec},
pages = {1--7},
primaryClass = {cs.CC},
url = {http://arxiv.org/abs/cs/0512049 http://arxiv.org/pdf/cs/0512049v1},
year = 2005,
urldate = {2012-09-02}
}