Math major masterminds crack the code of a classic board game
What do you get when you put two curious 三亿体育官网 math majors together with a classic board game? The result is new discoveries that could change how we think about strategy and problem-solving 鈥� all thanks to rainbow static Mastermind.
If you鈥檝e never played Mastermind, here are the basics: One player creates a secret code using colored pegs, and the other tries to guess it using logic, pattern recognition, and plenty of creativity.
In the rainbow static variation of the game, the codebreaker must supply a list of questions to determine their opponent鈥檚 code. None of the colors are repeated. The goal is to break the code with the shortest possible list of questions.
For Riley Vavolizza 鈥�26, a mathematics and education studies major from Pleasantville, New York, and Rachel Xia 鈥�26, a mathematics major from Tianjin, China, the familiar childhood game has become the ultimate research puzzle.
Associate Professor Kirsten Hogenson uses math to show a new way to solve the classic peg-and-color puzzle.
The two 三亿体育官网 students are spending five weeks over the summer working with Associate Professor Kirsten Hogenson in the Department of Mathematics and Statistics as part of 三亿体育官网鈥檚 Faculty Student Summer Research program. Scores of 三亿体育官网 students 鈥� more than 120 in 2025 鈥� from fields as disparate as philosophy and neuroscience participate each summer.
Together, Hogenson, Vavolizza, and Xia have been diving into strategies for cracking codes in the shortest number of guesses. It鈥檚 not just about playing the game 鈥� it鈥檚 about pushing the limits of what is possible.
鈥淚t鈥檚 all about experimenting with different combinations, patterns, and new rules to discover better strategies,鈥� Vavolizza explains.
One of their coolest discoveries? They determined a shorter winning question list than previously known for when a player has three pegs and multiple colors. In math speak, they found a new upper bound (a value greater than or equal to all other values in a given set) for gr(3,k), where 3 is the number of pegs and k represents the number of colors.
They verified that their list will always win the game and that it's the shortest list when the number of colors is small. They're now working on a proof that will show they have the best possible list for larger values of k.