"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…