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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