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2000 SMT/Advanced Topics Problems/Problem 1

Problem

How many different ways are there to paint the sides of a tetrahedron with exactly $4$ colors? Each side gets its own color, and two colorings are the same if one can be rotated to get the other.


SMT Solution

Assume we have $4$ colors - $1, 2, 3,$ and $4.$ Fix the bottom as color $1.$ On the remaining sides you can have colors $2, 3, 4$ (in that order), or $2, 4, 3,$ which are not rotationally identical. So, there are $\mathbf{2}$ ways to color it.




Credit

Problem and solution were taken from https://sumo.stanford.edu/old/smt/2000/

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