1. Rectangle A contains rectangle B. Must the perimeter of A >= the perimeter of B?

2. The 3-dimensional box (ie rectangular prism) A contains the 3-dimensional box B. Must the surface area of A be at least that of B? What about the sum of edge lengths -- can B be more edgy than A?

3. The n-dimensional box A contains the n-dimensional box B. The k-dimensional area of a box is the sum of the areas of all k-dimensional faces. For all n and k, must A's k-dimensional area be at least as large as B's?

I know the answer to the first two problems, but not the last one.

## Can't put a big box in a small box

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### Re: Can't put a big box in a small box

Here’s a quick, probably-could-be-made-rigorous, approach to the the k = n-1 subproblem:

**Spoiler:**

wee free kings

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