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Combinations: Unit gap in the interior of metal cube

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A CE graduate student named Naresh is experimenting with large concrete block sizes. For a block size of 1 foot high by 1 foot wide by 3 feet long, he tries to pack as many blocks as possible into a 7 foot by 7 foot by 7 foot metal box. He soon realizes that it is impossible. There will always be a 1 foot by 1 foot by 1 foot gap somewhere. In how many ways can this gap be in the interior of the blocks and not on an outside surface?

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So that it becomes easier to conceive the answer, solution also considers an example situation of a unit cube and a square surface with similar requirement as the question.

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So that this 1x1x1 foot^3 gap is not on an outside surface but somewhere in the interior of the blocks, this gap has to fall in the inner 5x5x5 foot^3 subcube of the ...

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