APMO

So APMO was last Monday, about a week ago. It was the only real proof-style competition I've done since MOP, so I didn't really know how well it would go, despite the fact that I had done some APMO problems. Regardless, I was happy that I could just sit down and do math.

After looking over all the problems, I decided to start with #3. It seemed at first that the answer was just $\binom{n-1}{2}$. It also seemed that I could come back to the problem later, so I tried #1. Usually I don't spend very much time on geometry because I can rarely actually do it, but I made pretty good progress and eventually solved it.

Afterwards, I tried #3 again. I completely trivialized the problem, and started to wonder whether APMO problems were really this trivial. However, the problem was actually this trivial.

After finishing these, I spent a lot of time on #2. I had the wrong idea at first - I was trying to start with a set that already summed to a 2009th power and change it to make it keep this property and gain the property that the product is a 2010th power. After trying the opposite method, the problem was quickly dispatched.

I spent my remaining time on the fourth problem, but my inability to do geometry seemed to have not been good for me on that problem. As a result, I estimate that my score is around 21, which seems to be a pretty common score.

Perhaps I should find out how to do geometry problems...