This year was a great year for the Danish IMO-team: We (I say “we” because I was deputy leader for the team) got our first gold medal, and as a team we beat our previous record, 77 points, by 13 point. In particular I was happy to see that we, together with China and US, was the best country on problem 5 (a problem that Tao thought was more challenging and interesting than problem 6). Denmark is usually in the second half on the country list, and even in a good year like this, we only beat 54% of the teams, so this is really remarkable. One reason, that we got that many points on problem 5 is, that is was a problem in combinatorics, and Denmark is usually good at combinatorics. Another reason is that problem 4 was a geometry problem, and Danes usually hate geometry! (remember that you get problem 1, 2, and 3 on day 1 and problem 4, 5, and 6 on day 2).
As you can see in the above link, Tao started a mini-polymath project about problem 5. So here you can see how a group of mathematicians worked together to solve that problem (and see the problem statement). I decided to ask some of the Danish contestants for a description of how they solved the problem, so that future contestants can see how a single person thinks. Here is Anders Eller Thomsen’s description. Edit: And here is Mathias Bæk Tejs Knudsen’s.