# Three colors to paint each side of a square, how many different squares?

1. Oct 13, 2011

### kaleidoscope

1. The problem statement, all variables and given/known data

If you have a square and can paint each side with one of three different colours, how many completely different arrays can you get? (rotated squares don't count)

2. Relevant equations

3. The attempt at a solution

I was thinking 3^4 / 4 but, that is not an integer, (3^4 - 1) / 4 is an integer but why would you substract 1?

2. Oct 13, 2011

### dacruick

You just have 4 edges of the square that you can colour? and does the order of the colours matter?

3. Oct 13, 2011

### dacruick

4. Oct 13, 2011

### HallsofIvy

Staff Emeritus
You might also want to consider if the same square rotated would counted as the same:
in other words would red, black, green, black be the same as black, red, black, green or different (both starting at the top of the square and going clockwise)?

5. Oct 13, 2011

### dacruick

I think my link will give you the information you need to solve it. I got an answer that I checked quickly by writing out all of the combinations.

6. Oct 13, 2011

### kaleidoscope

Thanks. I thought we needed a permutation.

7. Oct 14, 2011

### kaleidoscope

We actually need permutations and the answer should be around 24. I'm still looking for a solution.

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