Laser Cutting a Cube
Submitted by David Zimmerman
You have a unit cube of material in your lab. You take it to the laser
cutting table where you cut unit circles through the material, one
circular cut per each of the x, y & z axes. The cube doesn't fall
apart until after the third cut.
 How many pieces do you now have?
 How many are unique in shape?
 How many groups of same shaped objects are there, and how many per group?
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