Puzzle and Proof

Samuel Dittmer is a three-time USA Mathematical Olympiad qualifier and two-time William Lowell Putnam Mathematical Competition honorable mention from Indiana who has also lived in Albania. Sam won the national competition of the American Regions Mathematics League during his sophomore year in high school. Sam graduated with a PhD in math from UCLA in 2019. He lives with his wife and dog in Los Angeles. Hiram Golze is a math teacher at the Waterford School. He grew up in Utah, where he won the Utah State Math Contest twice and qualified for the USA Mathematical Olympiad once. He currently coaches the Utah American Regions Mathematics League Team and has coached the Utah state MATHCOUNTS team. During the summers, he teaches at the AwesomeMath Summer Program. He has a master’s degree in math from the University of Illinois at Urbana-Champaign. Grant Molnar grew up in North Carolina. As an undergraduate, he tied for third place in the Virginia Tech Regional Math Competition, and served as Brigham Young University Putnam Team Captain from 2014 to 2016. He graduated with his PhD in math from Dartmouth in 2023, and now works as a software developer. Caleb Stanford is currently an assistant professor of computer science at UC Davis. He grew up in Utah, where he won the Utah State Math Contest five times and qualified for the USA Mathematical Olympiad once. He holds a bachelor’s degree in math and computer science from Brown and a PhD degree in computer science from the University of Pennsylvania. He currently lives in the San Francisco Bay Area with his wife and two cats.

1. Introduction. 1.1. History. 1.2. The Problem. 1.3. Grading and Results. 1.4. Structure of the Book. 1.5. Acknowledgements. 2. Problems. 2.1. Discrete Structures. 2.2. Counting and Probability. 2.3. Games. 2.4. Algebra. 2.5. Number Theory. 2.6. Geometry. 3. Solutions. 3.1. Discrete Structures. 3.2. Counting and Probability. 3.3. Games. 3.4. Algebra. 3.5. Number Theory. 3.6. Geometry.