Playing it Smart

U of G researchers create artificial intelligence models that ‘learn’ to solve math puzzles.

Math is a powerful tool that can be used to solve real-world problems. This is accomplished by breaking down the problem into its component parts, then using mathematical terms to explain each component—developing a mathematical model of the problem. There are many types of mathematical models, including neural network models. 

Neural network models try to imitate how our brains work, by passing information across a network of interconnected ‘cells’ or processing units to learn a task, such as solving grid-based math puzzles like Sudoku. The neural network learns how to play the game; it places numbers on the grid and eventually fills the entire grid to find the correct solution. However, when we change the type of math puzzle, the rules change, and the neural network model must be adapted. 

University of Guelph mathematics professor Herb Kunze and his students, Bryson Boreland and Gord Clement, recently established that neural networks can solve Sudoku and KenKen puzzles. Very recent work by Dr. Kunze and his student, Maxwell Fitzsimmons, proved that neural networks can be combined into ‘hybrid’ networks, which can be used to solve new problems, in this case two other types of grid-based math puzzles, Kakuro and Akari (also called Cross Sums and Light Up, respectively). There are a variety of neural network models that have been developed. Each one understands a specific set of rules. For example, in Sudoku, one rule is that each row must contain all numbers from 1 to 9. Dr. Kunze and his students found that their networks could successfully solve these puzzles. Interestingly, they observed that the neural network enters its first several decisions into the grid in the same order as a human solver. 

“Our hope is that this research will inspire fellow researchers to think creatively about the different ways to use neural networks,” says Kunze. “Using neural networks to solve math puzzles like Sudoku, KenKen, and Akari could also be a dynamic and engaging way to learn about neural networks and artificial intelligence in a classroom.”

This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC). 

Fitzsimmons, M and Kunze, H. Combining Hopfield neural networks, with applications to grid-based mathematics puzzles. Neural Networks. 2019. doi: 10.1016/j.neunet.2019.06.005