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

Your solutions presuppose that the cubes are identical; this is not the
case in Instant Insanity. If they are all distinguishable you are
missing a factor of $N!$.
The smaller possible solution is valid under the assumption
that a stack is regarded as identical with that stack 
produced by turning the original stack upside down. The larger
solution regards these two stacks as different.
