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Cube the Cube (Posted on 2004-10-02) Difficulty: 5 of 5
Remember Square Divisions? This problem demonstrates the deconstruction of a square into smaller squares with integer-length sides.

Given a cube with edge length 60, can you find a deconstruction of the cube into smaller cubes (none of which are alike) with integer length sides (or prove it can't be done)?

No Solution Yet Submitted by SilverKnight    
Rating: 2.6667 (3 votes)

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Hints/Tips 30 or 31 unit cube is essential | Comment 8 of 12 |

If it is possible to solve

The volume of small cuThe volume of 60 unite cube is 216 000

The volume of cubes from 1-30 = 216 225

The max volume of cubes until 31 = 219 016

If any bigger cube is used, the max volume is less than 216 000, therefore either a 31 or a 30 unit cube must be in the final solution.

 

However I wonder if there is any...


  Posted by Detti on 2004-10-08 12:10:44
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