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Pushing objects through holes in other objects

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A classic problem is to push the largest possible cube through a square hole in a unit cube. That solution involves hexagons and involves the same calculation as finding the area of the

The late inventor of "recreational mathematics" Martin Gardner believes he was the first to take things to a higher dimension by asking for the largest cube that will fit entirely inside a unit hypercube. I know the answer but I would not attempt its derivation myself. This would be one of the more difficult puzzles ever posted on Brain Den. Even the coveted bonanova gold star seems too small a prize for anyone who finds the answer.

It's on m172.

Happy hunting. ;)

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Question is why would I go around pushing cubes in holes that are in other cubes?

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To be the first on your block, perhaps. Otherwise I don't know. :)

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