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October 26th, 2017, 07:14 PM   #1
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Block by block

Take a cube built of 125 unit cubes. How many distinct cubes (1x1x1, 2x2x2, 3x3x3, 4x4x4 and 5x5x5) can be made by facing the unit cubes?
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October 27th, 2017, 03:54 AM   #2
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What does "facing the unit cubes" mean?
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October 27th, 2017, 04:43 AM   #3
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There enough 1x1x1 cubes to make 4 3x3x3 cubes:
125 - 27 - 27 - 27 - 27 = 17 (leftovers).
Is that what you mean?
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October 27th, 2017, 10:28 AM   #4
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By "facing" I meant "building into a unique cube."

If I started with a 3x3x3 cube, I would have from it 27[1x1x1]+8[2x2x2]+1[3x3x3]=36 unique cubes.

The counts are not always cubic {1, 8, 27} like in this example -- as a 4x4x4 or greater largest cube would show.

A 4x4x4 cube would manifest 100 cubes overall, I believe.
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October 27th, 2017, 10:33 AM   #5
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You've lost me...take over and manifest, Country Boy
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