An Icosahedral Edge Coloring Problem

The 2017 Putnam Mathematical Competition Problem A6:

The 30 edges of a regular icosahedron are distinguished by labeling them 1, 2, …, 30. How many different ways are there to paint each edge red, white, or blue such that each of the 20 triangular faces of the icosahedron has two edges of the same color and a third edge of a different color?

This was a side project for the Department of Mathematics at HKU, under the supervision of Dr. Y. K. Tai, during the summer of 2023. An interesting part of this combinatorial problem is its use of linear algebra, particularly the concepts of finite vector space and linear map.

I have made a full video about the solution. To see the full video, here is the link. This video production was created using Manim, a Python library for creating mathematical animations. The code can be found here.

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