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 $8 \cdot 15 = 120$, 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
This post has been edited 2 times. Last edited by v_Enhance, Aug 14, 2012, 6:21 PM

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lol I did the entire day 2 in 15 minutes -_- (obviously not writing up formally, more like you do this, that and then this, trivial, but I at least checked out the details)

day 1: problem 1 woah $a_n$ is isloated. hmm WLOG set it to $0$ in worst case.
...oops silly problem.
problem 2 since I am atrocious at geometry I did not solve part 2 within like 10 minutes, took me like 40 -_-
problem 3 took me literally 2 minutes to do+write-up.
problem 4 I refuse to do the casework. the problem is actually just notice since you have small numbers, go bash out the cases in terms of number of blacks.

so day 1 was slightly hardish due to my bad geometry skills, but day 2 was a joke.
This post has been edited 2 times. Last edited by dinoboy, Aug 14, 2012, 9:59 PM

by dinoboy, Aug 14, 2012, 9:58 PM

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The "cases" for problem four were hardly cases; basically you just notice that $b \le 4$ is trivial, so now you're left with $b=5$ and $b=6$, both of which can be solved with the same idea. The computations are $\binom{5}{2} + 5 > 13$ and $\binom{6}{2} > 15$, respectively. The meat of the problem is definitely the idea to look at midpoints, which took me very long to realize.

by v_Enhance, Aug 14, 2012, 10:09 PM

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wait isn't the slightly obvious that you need to realize that, since how else are you going to swap points and successfully get a symmetry line thingy

by dinoboy, Aug 14, 2012, 10:23 PM

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Confirmed: I suck at combo :P
I was trying to do stuff with arithmetic-free sequences in $\mathbb F_{13}$ and similar nonsense, or trying some global nonsense with probalistic method, which got me nowhere.

by v_Enhance, Aug 14, 2012, 10:31 PM

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lol, interesting, you don't barybash any of the geo anymore?! :P :wink: :wink:

yeah and number 1 reminded me of IMO#2 too(2 too lol).

by icantdecide, Aug 18, 2012, 5:01 AM

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i know someone who went to CGMO and she saids gold was not positive.

by icantdecide, Aug 18, 2012, 5:03 AM

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i know someone who went to CGMO and she saids bronze was not positive.

by icantdecide, Aug 18, 2012, 5:03 AM

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