Problem: Given 5 colors to choose from, how many ways can we color the four unit squares of a $2\times 2$ board, given that two colorings are considered the same if one is a rotation of the other?
I saw an existing thread on this question but the answers used Burnside's Lemma, but I am not familiar with Group Theory (and I don't think it is necessary for this problem).
I know how to do this problem if each square on the board must be a different color: There are $5*4*3*2$ possible colorings for the four unit squares and we just divide that amount by 4 to account for rotationally similar arrangements.
However, this problem implies that all squares can be the same color, so I am unsure how to do it.