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No Unit Cube Dissection (Posted on 2015-06-11) |
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Find a dissection of a 19x19x19 cube such that all the pieces are cubes with integer dimension and none of them are unit cubes.
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Submitted by Brian Smith
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Solution:
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The dissection takes the following cubes:
2 7x7x7
1 5x5x5
54 4x4x4
96 3x3x3
16 3x3x3 plus 9 4x4x4 cubes can be assembled into a 12x12x7 brick. Make six of these bricks. The 5x5x5 goes in the center, the two 7x7x7 go in opposite corners, and the 12x12x7 bricks fill in the remaining space. |
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