Great problems! I feel like Ibwould be able to solve them yet I cant... After the competition, will you post the solutions?

Edit: In problem 1, I did notice that the p(x) starts with (x\^18 - 1) and then (x\^2 -1) where after the exponent of x increases to (x\^16-1), is this a mistake/typo? Or is it actually meant to be (x\^18 -1) ?

I am also a bit confused about problem 8, as english isnt my first language and therefore don't know what is meant by *"such that the tiling doesn’t*

*decompose into a tiling of two smaller rectangles?"*