You lied a bit week ago :D. "You have plenty of time to try your hand at the hardest problems of 2016, as the contest runs until January 10. The solutions for two problems were described in this blog, so you can get a head start :)" but just within those five problems there are three which are on Prime New Year contest :D. I can hint you that your analysis to "Edit" problem contains a mistake (however easy to fix, so that's not a big deal), maybe that's the reason you submitted it and got WA ;p. I tried to solve that problem for few hours and I finally surrendered and I decided to read your analysis and I read there exactly what was an idea of one of my solutions which I disregarded because it was simply wrong, so I didn't learn a lot by reading it. However it gave me faith it can lead to correct solution :D. And it really lacked just an easy fix.

It's hard to choose just one out of those problems, but my vote goes to 0.636, combinatorial geometry is great and it is its shining gem ;p. Apart from those, probably there are many great problems from 2016 which I would like to mention as my favourites, but just one comes to my mind right now — Dancing Disks from recent CERC.

OK, I searched a bit and recalled two problems which I exceptionally liked. One is Railway from IOI, second one is your problem "Freeform Factory" from GCJ https://code.google.com/codejam/contest/10224486/dashboard#s=p3 :)