
Help with combinatorics?
I have recently completed a problem, however under second inspection, I fear I may need to include something. Here is the problem: How many different ways are there to colour the $\displaystyle 1*1$ squares of a $\displaystyle 3*3$ board using $\displaystyle 4$ colours so that $\displaystyle 1*1$ squares that share an edge or corner receive different colours?
I have written an answer for this and I have written solutions both including and excluding rotations and reflections, however I am not sure whether I need to include anything about whether colours are "distinct". What I mean by "distinct" is that if you have found a way of colouring the $\displaystyle 3*3$ grid and then swap 2 or more sets of colours in that individual grid, then the resulting grid is unique if the colours are considered "distinct" and not unique if the colours are not considered "distinct".