On Saturday, December 4, four students represented APU in the 82nd Putnam Competition, the preeminent mathematics competition for college students in the United States and Canada. Geneva Boersema, Emily Gottry, Kathryn Tickle, and Benet Zheng competed for six hours alongside thousands of students at hundreds of colleges and universities. Two of the twelve problems are reproduced below:
A1: A grasshopper starts at the origin in the coordinate plane and makes a sequence of hops. Each hop has length 5, and after each hop the grasshopper is at a point whose coordinates are both integers; thus, there are 12 possible locations for the grasshopper after the first hop. What is the smallest number of hops needed for the grasshopper to reach the point (2021, 2021)?
A3: Determine all positive integers N for which the sphere x^2+y^2+z^2=N has an inscribed regular tetrahedron whose vertices have integer coordinates.
Please join us in congratulating these students for their brave efforts! We look forward to receiving the results in late February. Kudos to Dr. Bryant Mathews, Professor in the Department of Mathematics, Physics, and Statistics, for organizing and supporting the APU Team, along with assistance from Dr. Sharon McCathern, Associate Professor in the Department of Mathematics, Physics, and Statistics, on the day of the competition.
