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Cube partition

  1. Oct 14, 2007 #1
    Can you describe any partition of a cube in to smaller cubes that are not the same size? (I know a few answers to this one...)

    It is easy to think of 8 identical cubes being combined to make one big cube. But, if the cubes don't have to be the same size: is there another way to do it? (I think I know the answer)

    Can you describe any partition of a cube in to smaller cubes that are not the same size and that are not based on divisions of the larger cube in to regular grid? (no idea)

    Can you describe a partition in to cubes where every cube is a different size? (no idea)
     
  2. jcsd
  3. Oct 14, 2007 #2
    not sure if i got your question
     
  4. Oct 15, 2007 #3
    Yes, it's perfectly easy to do this. Imagine a cube 3 units on each side. Make 3 cuts to create a cube 2 units each side, leaving another cube 1 unit each side, 3 boxes of size 1 by 2, and 3 boxes size 2 by 2. Then cut these boxes into cubes of size 1 by 1. That's just one way.
     
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