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- From: alopez-o@neumann.uwaterloo.ca (Alex Lopez-Ortiz)
- Newsgroups: sci.math,news.answers,sci.answers
- Subject: sci.math FAQ: Master Mind
- Followup-To: sci.math
- Date: 17 Feb 2000 22:55:52 GMT
- Organization: University of Waterloo
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- Summary: Part 22 of 31, New version
- Originator: alopez-o@neumann.uwaterloo.ca
- Originator: alopez-o@daisy.uwaterloo.ca
- Xref: senator-bedfellow.mit.edu sci.math:347387 news.answers:177507 sci.answers:11215
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- Archive-name: sci-math-faq/mastermind
- Last-modified: February 20, 1998
- Version: 7.5
-
-
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- Master Mind
-
-
-
- For the game of Master Mind it has been proven that no more than five
- moves are required in the worst case.
-
- One such algorithm was published in the Journal of Recreational
- Mathematics; in '70 or '71 (I think), which always solved the 4 peg
- problem in 5 moves. Knuth later published an algorithm which solves
- the problem in a shorter number of moves - on average - but can take
- six guesses on certain combinations.
-
- In 1994, Kenji Koyama and Tony W. Lai found, by exhaustive search that
- 5625/1296 = 4.340 is the optimal strategy in the expected case. This
- strategy may take six guesses in the worst case. A strategy that uses
- at most five guesses in the worst case is also shown. This strategy
- requires 5626/1296 = 4.341 guesses.
-
- References
-
- Donald E. Knuth. The Computer as Master Mind. J. Recreational
- Mathematics, 9 (1976-77), 1-6.
-
- Kenji Koyama, Tony W. Lai. An optimal Mastermind Strategy. J.
- Recreational Mathematics, 1994.
- --
- Alex Lopez-Ortiz alopez-o@unb.ca
- http://www.cs.unb.ca/~alopez-o Assistant Professor
- Faculty of Computer Science University of New Brunswick
-