Path: senator-bedfellow.mit.edu!bloom-beacon.mit.edu!newsswitch.lcs.mit.edu!netnews.com!europa.netcrusader.net!204.71.34.3!newsfeed.cwix.com!torn!watserv3.uwaterloo.ca!alopez-o 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 Lines: 37 Approved: news-answers-request@MIT.Edu Expires: Sun, 1 Mar 1998 09:55:55 Message-ID: <88hu9o\$r5s\$1@watserv3.uwaterloo.ca> Reply-To: alopez-o@neumann.uwaterloo.ca NNTP-Posting-Host: daisy.uwaterloo.ca 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 Archive-name: sci-math-faq/mastermind Last-modified: February 20, 1998 Version: 7.5 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