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Cutting
the Cube
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Strategies and Hints
Mr. Lim would need 6 cuts to get 64 1-inch cubes. You need to determine the minimum number of cuts necessary along the three discrete sides if you did not rearrange. Look at the illustration of a 4 x 4 x 4 solid.
When you rearrange, the minimum is found by cutting each edge as nearly in half as possible, putting the pieces together and cutting as nearly in half again until you get a solid with a unit dimension. Now restack the solids into the 4 x 4 x 4 solid and repeat the procedure for the second and then the third sides. When you complete the three sides, you will have 1 x 1 x 1 cubes. Therefore, the sum of the cuts is the answer. (See picture for the second cut of the 4 x 4 x 4 solid).
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rearrange
to a |
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