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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.


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
Fri Feb 20 21:45:30 EST 1998