Using Integer Programming to Solve Games, Puzzles, and Ciphers

In this paper, we introduce three different classes of undergraduate research projects that implement model building and integer programming. These research projects focus on determining and analyzing solutions to the game The Genius Square, optimizing allocation of trains to maximize points in the game Ticket to Ride, and (code)breaking monoalphabetic substitution ciphers. Initial models and analyses for these scenarios that came from previous undergraduate research projects are shared along with a variety of open research questions.