@ideparada: comments on sheet 2

[julian-upc]

Problem 1

You actually don't prove that the edges of the permutahedron correspond to adjacent transpositions! So you don't really know that the polytope is simple. But otherwise, the exposition is very nice and detailed. Thanks!

Problem 2

Congratulations! You solved the problem. Here is a prize for you:
http://arxiv.org/pdf/math/0406224
However, I missed where you use Pick's Theorem.

Problem 3

Thanks for the nice research! You missed the issue with the unencrypted metadata, though.