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Welcome to the Mind series 2nd edition, comprising openMind and masterMind

Irving subsequently found a strategy with slightly smaller average length. Koyama and Lai described a strategy that minimizes the average number of guesses, requiring on average 4. A slight modification also described by Koyama and Lai increases the average to 4.

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The "static" problem of finding the minimum number of guesses the codebreaker can make all at once at the beginning of the game without waiting for the answers, and then upon receiving the answers, completely determine the code in the next "guess" Chvatal , can be solved with six initial guesses Greenwell One particular combination that allows the codebreaker to know the code after six guesses and so require a seventh to reveal his knowledge of the solution is 1, 2, 2, 1 , 2, 3, 5, 4 , 3, 3, 1, 1 , 4, 5, 2, 4 , 5, 6, 5, 6 , 6, 6, 4, 3.

It is not known if this number can be reduced to five exhaustive checking would require computations , although it is believed not. Swaszek gives an analysis of practical strategies that do not require complicated record-keeping or use of a computer. Making a random guess from the set of remaining candidate code sequences gives a surprisingly short average game length of 4. Bewersdorff, J.

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Greenwell, D. Guy, R. Guy and R. Washington, DC: Math.

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Irving, R. Knuth, D.

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