“Consider an icosahedron with every edge labeled from 1 to 30. Color these edges red, white, or blue, such that no face has all three edges the same color or all three faces the same color. How many ways are there to do this?”
If you can solve this problem, you might have what it takes to participate in the annual William Lowell Putnam Mathematical Competition, a preeminent mathematics competition for undergraduate college students.
“The problems themselves are very difficult, often asking us to demonstrate that a general statement is true rather than to solve a specific problem, or if we do solve a specific problem, it is often a very complicated problem,” said competitor Sam Bidwell ’21. “For this particular question, which appeared on last year’s test, the solution involves complicated mathematics that I do not have the experience to properly explain within even five paragraphs to anyone who had not taken the prerequisite class, which was, as I recall, Abstract Algebra 2.”
Bidwell, along with Di Chen ’20, Haochen Gao ’21, Joe Cutler ’21, Morgan Long ’22, and Yaqian Tang ’21 were among 4,623 students from the U.S. and Canada to participate in the 2018 competition. Chen and Gao ranked in the top 500 individual competitors; and a team consisting of Bidwell, Chen, and Gao was ranked 27th out of 568 institutions (within the top 5 percent).