Partitioning a Cube into Unequal Size Cubes: Can it be Done?

[futurebird]

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

Can you describe a partition into cubes where every cube is a different size? (no idea)

 

[akhil982]

not sure if i got your question

 

[daveb]

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.