Painting a Tetrahedron
Each face of a regular tetrahedron is painted one of 4 available colours; colours may repeat and need not all be used. Two painted tetrahedra are the same if one can be rotated to match the other (reflections are not allowed). How many different painted tetrahedra are there? Give an integer.
Related problems & prerequisites
Worth solving first
- Colouring the Edges of a Cube 6.0/10
- Black and White Corners 6.0/10
- Rotating a Three-by-Three Grid 6.0/10
Source: Standard application of Burnside's lemma; no traceable original source. Statement written for AxiomIQ.