Number of ways to stack N cubes I'm trying to figure out how many ways are there to stack N cubes on top of each other.
Once you get a particular stack of 4 cubes let's say, the order of the cubes doesn't matter, just which sides are being shown does.
I'm generally finding 2 numbers: 
1.) 6 * 24^(n-1)
and
2.) 3 * 24^(n-1)
Which is the correct answer, and why?
To understand the question better, you can refer to the Instant Insanity puzzle:
http://en.wikipedia.org/wiki/Instant_Insanity

I suspect that the Wikipedia article's number of $41,472 = 24^4 / 8$ arrangements of the four cubes comes from the idea that each of the four cubes can have 24 orientations.  However, the whole stack can be rotated into any of four positions, removing a factor of 4 without altering the four visible side face patterns.  
In addition, the whole stack can be turned upside down (or equivalently, since order does not matter, each cube can be turned upside down) without altering the four visible face patterns, just whether you encounter them clockwise or anti-clockwise. That removes a further factor of 2.  
So Wikipedia uses your $3 \times 24^{n-1}$ answer.
