CGMO Ramblings
by v_Enhance, Aug 14, 2012, 6:15 PM
Anyways, first of all, gj USA team! Results are here. Problems are here.
Scores are
, but only multiples of three are given (lolwhat). Scores were quite high this year: gold cutoff was 108, silver cutoff was 75. There's a rumor that bronze cutoff was not positive.
I did Day 1 in test conditions, although I only gave myself two hours. I got 134 and the first half of 2 in that time. I looked at 5678 later that day as well. Some thoughts on the questions: overall I thought day 2 was borderline trivial, and day 1 was relatively easy (not outlandishly so, though).
Day 1
Day 2
Scores are

I did Day 1 in test conditions, although I only gave myself two hours. I got 134 and the first half of 2 in that time. I looked at 5678 later that day as well. Some thoughts on the questions: overall I thought day 2 was borderline trivial, and day 1 was relatively easy (not outlandishly so, though).
Day 1
- 10 minutes. Reminded me of IMO2 both when I first saw it, and when I solved it. The difference is that the estimate
is actually extremely motivated (one does not lose any strength), and suddenly the inequality becomes an equality! Pretty amusing. I guess this was OK for a #1 if only for intimidation factor.
- 25 minutes. I have a confession to make: I only now learned the exterior bisector theorem. Part 1 was pretty okay, albeit trig-bashable. I mis-copied part 2 during my test run, so I'm glad I moved on to #3 after only 15 minutes or so. Overall, this should have been a moderate-easy geo.
- 15 minutes. I was pretty frightened when I first guessed the answer, but it turned out to be not that bad. I just took
, and put in
and
popped out with a few manipulations. During the test I thought that this would be a medium-hard NT, but afterwards I realized you could just use
(oops) and
Euler'sFermat's Little Theorem; this seems substantially more natural, and probably meant that this was actually medium-easy. - 70 minutes. I quite liked this problem, despite my terrible combinatorics skills. I was also pretty proud of myself for solving it. Other people I talked to said it wasn't hard though. More than anything this confirms that I suck at combo.
Day 2
- Very easy. Even without fact 5, the in-scale diagram provided on the test really gave it away.
- Easy if you know
. A bit of color-chasing on
solved it.
- Just draw a picture! The result becomes obvious if you plot
and
.
- This definitely favors knowledge over intuition. It was also a rather computational. I could see this as a hard AIME #15; it definitely is a good fit for the AIME in general: a few somewhat standard tricks, then compute.
This post has been edited 2 times. Last edited by v_Enhance, Aug 14, 2012, 6:21 PM