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