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 October 26th, 2017, 07:14 PM #1 Senior Member   Joined: May 2015 From: Arlington, VA Posts: 403 Thanks: 27 Math Focus: Number theory 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?
 October 27th, 2017, 03:54 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 What does "facing the unit cubes" mean?
 October 27th, 2017, 04:43 AM #3 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,412 Thanks: 1024 There enough 1x1x1 cubes to make 4 3x3x3 cubes: 125 - 27 - 27 - 27 - 27 = 17 (leftovers). Is that what you mean?
 October 27th, 2017, 10:28 AM #4 Senior Member   Joined: May 2015 From: Arlington, VA Posts: 403 Thanks: 27 Math Focus: Number theory 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.
 October 27th, 2017, 10:33 AM #5 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,412 Thanks: 1024 You've lost me...take over and manifest, Country Boy

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