### USAMO!

Whew - this week has been crazy. And I think we all know why ... it's USAMO time! Or was ...

Fortunately, I was able to talk to Messrs Block and Micek, and negotiated my ability to take the USAMO, but at great cost. The first day I had to take the USAMO in Micek's classroom ... while freshmen were taking the STAR testing. They were loud, to say the least, and I could focus only with great difficulty, at least until 12:20 (3:20 ET - that is, 1:40 before time was up) when the freshies left. (But don't worry, I didn't break any rules - I was proctored and I didn't chat.) This may explain my relatively poor performance on Day One.

The second day was easier, as I was able to negotiate taking the test in the library (don't worry, oh eagerly pissed-off USAMO graders, I was indeed proctored), and I performed much better. Big surprise.

I was quite out of shape mathematically. I had only started practicing seriously for the USAMO about a month before, and I couldn't seriously hope to do very well with so little practice. Of course, taking old tests is a little pointless if you can't solve a single problem... ;) In this regard, I think I did much better than I expected - in the immortal words of Ubemaya, "my goal is a non-negative score, although I'd be happy to get a negative score also."

My equipment wasn't the best either. The first day I took my dad's expensive Byelorussian sketching kit, but unfortunately the compasses there were rather dull, as they had not been used for quite awhile. Keeping this in mind, I took my own, much smaller compass set the next day, only to understand why I hadn't taken it the first day - the quality was so bad that I could hardly use them, and the set did not include a protractor, just when I needed one (for problem six, I finally had to resort to constructing right triangles on graph paper and then tracing 60 degree angles to draw a neat equilateral triangle). Once again Staedler's quality shows me why those guys should just stick to making erasers ...

But enough about working conditions. Time to talk about the problems!

As I mentioned earlier, I didn't do too well on the first day, partly because of the friggin freshmen, and partly because of my own stupidity of course. I immediately jumped ahead and solved the second problem, taking something like two hours to write up an incredibly neat, incredibly detailed solution - only to realize after faxing the solutions that I was supposed to find a circle with radius sqrt(2)/2, not a square with side length 1! Well, I hope I'll get two or three points, because other than this my solution is a pretty good one. Next, I attacked problem one, finding out some facts and then hitting a brick wall - I submitted some hastily done formulae in hope of maybe one point. And problem three - that I could hardly understand, let alone find a way to solve. Total for Day One: 3-4 points of a possible 21.

The second day I performed much better. I solved Problem Four satisfactorily, for six, maybe even seven points. The great thing about Problem Four was that it asks for an answer - 8025 - so I KNOW I got the problem right! =) And I proved the equilateral equality for #6, though I did not make any headway into proving the general inequality: I'm hoping for one or two points for the equality. Problem Five I stared at and stared at, but couldn't solve, as, I imagine after seeing the solution, neither could 99% of test takers. Total for Day Two: 7-9 points of a possible 21.

So, in total I got 10-13 points, which isn't bad at all for someone who expected to get zero (see my previous post for details about all that). After a little practice, and hopefully without interference from pesky freshmen, I may even qualify for MOP next year! (18-20 points needed to qualify for sophomores and juniors)