**Problem of the Week-6: Coloring the Square **

In how many ways can the corners (vertices) of a square can be colored using at most 5 colors, where any two colorings are considered the same if one can be obatined from the other by reflections or rotations (or both)? (Note that a vertex is dimensionless so it is more proper to say we are assigning colors to vertices. Also assume that no vertex is left uncolored.)

Explain your answer.

Posted: 11/26/06

Submit your answers (by e-mail or hard copy) before 4 pm on 11/17/06 to Noah Aydin.

Mathematics Dept.