2000 SMT/Advanced Topics Problems/Problem 1

Problem

How many different ways are there to paint the sides of a tetrahedron with exactly 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 colors - and Fix the bottom as color On the remaining sides you can have colors (in that order), or which are not rotationally identical. So, there are ways to color it.

Credit

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