In November 2004, Michiel de Bondt proved that solving a Mastermind board is an NP-complete problem when played with n pegs per row and two colors, by showing how to represent any one-in-three 3SAT problem in it. He also showed the same for Consistent Mastermind (playing the game so that every guess is a candidate for the secret code that is consistent with the hints in the previous guesses).[17][better source needed]
The Mastermind satisfiability problem is a decision problem that asks, "Given a set of guesses and the number of colored and white pegs scored for each guess, is there at least one secret pattern that generates those exact scores?" (If not, then the codemaker must have incorrectly scored at least one guess.) In December 2005, Jeff Stuckman and Guo-Qiang Zhang showed in an arXiv article that the Mastermind satisfiability problem is NP-complete.[18][better source needed]
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