Algorithm to Prove Formulas for the Expected Number of Questions in Mastermind Games

Abstract

We close the gap in the proof (published by Chen and Lin) of formulas for the minimum number of questions required in the expected case for Mastermind and its variant called AB game, where both games are played with two pegs and $n$ colors. For this purpose, we introduce a new model to represent the game guessing process and we develop an algorithm with automatizes the proof. In contrary to the model used by Chen and Lin, called graph-partition approach, which is limited to two pegs, our model and algorithm are parametrized with the number of pegs and they could potentially be used for any number of pegs.