Mastermind

The commercial game called “Mastermind ” can be used to teach a number of mathematical and logical concepts. This paper discusses the game and various strategies not only to play the game, but to teach some mathematics using the game as an example. Invicta Plastics was the original producer of the game in 1971 and it holds the worldwide Trademark for the name. Here we study the game with 4 slots and 6 colors, although other versions are obviously possible. 1 The Game Mastermind is a game played between two people. One selects a secret code and the other makes successive guesses to determine the secret code by making guesses for each of which the first person gives an indication of how close the guess is. The code is a sequence of four colors chosen from a set of six as is each guess. In the physical game, there are colored pegs that fit into four adjacent holes. The colors may repeat in the sequence, so altogether, there are 64 = 1296 different possible codes (and guesses). The colors vary in different versions of the game, so we will arbitrarily use these six: red, green, blue, yellow, cyan and purple. In this paper, if we just want to talk about a general sort of position, we may just use the numbers from 1 to 6 to represent the colors. Thu