1. The problem statement, all variables and given/known data How many regular tetrahedrons (of the same dimension) can you distinguish using 4 different colors to paint all of its 4 faces? 2. Relevant equations 3. The attempt at a solution I got to 36, but I am not confident about my answer because I used mostly "real world" intuition. How can I model this mathematically? If I used one color each time I could only paint the whole tetrahedron using that one color. So that's 4 different tetrahedrons right there, one of each different color. If I used two different colors I could paint one face using the first color and still have 3 options for the remaining 3 faces. So that's 4*(3), 12 more options. I could also paint two faces using one color and the other two using another. But then I would get some similar tetrahedrons by simple rotation. How can I model this??