Student Research Projects

The New Mastermind

Student Samantha Eanes '15, Tyler Chang '16, & Thomas Simmons '16
Faculty Mentor(s)
Department Mathematics
Course MATH 489: Undergraduate Research


Mastermind is a popular code-breaking board game in which a player attempts to determine a hidden sequence of colored pegs by laying out guesses. In the traditional board game, one player creates the hidden code using 4 pegs available in 6 colors, and the other player tries to guess the hidden code in fewer than twelve guesses. In 1977, computer scientist Donald Knuth published his now famous paper detailing a strategy that would win the original Mastermind game with 4 pegs and 6 colors in five of fewer moves. Lately new versions of the game have been appearing on iPad apps that vary components of the game, including number of pegs, number of colors, whether or not repetition of colors is allowed, and feedback given to the player. In this poster, we present how enhanced feedback affects the number of moves required to win, and we give formulae for the number of unique first moves and number of possible responses to given moves when the number of pegs and/or colors vary.


Presented at the joint meeting of the American Mathematical Society & Mathematical Association of America in Baltimore, Maryland, January 2014.


Project took 2nd place at VWC's annual 2014 Undergraduate Research Symposium, Division of the Natural Sciences and Mathematics