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Different Colored cube


This is an interesting puzzle which I had seen somewhere
else. My solution was almost the same except that I visulized a vector or an arrow "attached" to one surface
vertically. One can see that for any given paint situation,
the vector can point to 6 direction +/-X, +/-Y and +/-Z.
And for each direction the vector can spin 4 ways 90 degree each. That means that there are 6*4 choices that
are repeated and the answer 6! / 24 =30 is correct!

It is interesting to examine the same puzzle for a triangle
pyramid with 4 different color to paint with.
For any given paint situation a vector vertical to one
surface can point to 4 different directions in the space.
And for each direction it can spin 3 ways 120 degree each.
So the total different painted cubes in this case are:
4! / 4*3 = 2. Only two different cubes can be created.

Aharon Tam
Friday, July 25, 2003

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