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# Pushing objects through holes in other objects

2 replies to this topic

### #1 bonanova

bonanova

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Posted 24 September 2013 - 03:55 AM

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 largest square that can fit entirely inside a unit cube.

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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Vidi vici veni.

### #2 Anza Power

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Posted 24 September 2013 - 09:42 PM

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

bonanova

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Posted 25 September 2013 - 12:06 AM

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