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

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kaleidoscope
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Homework Statement



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)

Homework Equations


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?
 
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You just have 4 edges of the square that you can colour? and does the order of the colours matter?
 
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)?
 
kaleidoscope said:
(rotated squares don't count)

HallsofIvy said:
You might also want to consider if the same square rotated would count

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.
 
dacruick said:
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.

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