The last of two competition days is over. Can't say I'm satisfied with my performance. Day 1: spent too much time banging my head on problem 2 (concerning polynomials), I had a slightly wrong approach that lead to some tricky special cases in an otherwise simple inductive proof. Starting from scratch probably would've gotten me on the right track, as the solution really was pretty simple. After all this hassle all the points I got were 10 (out of 20) from a solution to problem 4 that I cobbled up in the last 15 or so minutes.

On day 2 I was close to the solutions of three problems but just couldn't make it, mostly because of spending too much time on problem 3. I somehow managed not to spot that the combinatorial sum in prob 3 was just the binomial expansion of the analytic solution to the fibonnacci reccurrene, a fact that would've instantly provided the solution.

Also, I didn't look too closely at the geometry problem as geometry tends not to be my forte. I however did manage to spot that the points in question must lie on a hyperbola. This fact combined with the obvious symmetries of the situation would've given that the points actually lie on a line, yielding the solution.

Guess it's just been too long since I've solved any real math problems.

Tomorrow: excursion to a monastery. The day after that: prize ceremony. We're arriving in Finland on Thursday night.

I'll link to the problems when they hit the interwebs.