iTest TOC Statistics -- First Two Rounds

I just got done reviewing statistics for the first couple of rounds of the 2008 iTest TOC. At first, I just wanted to look through them for the fun of it, but as soon as I did it occurred to me that I should take the opportunity to think about how hard the problems are for each round's competitors. This helps me know how hard to craft future problems.

Similarly to last year, I wrote nearly all the problems for the first three rounds (unlike last year, I split duties with Adam Hesterberg and Zach Abel for the last three rounds -- just the three hard geometry problems were due to Zach last year). The problems are intended to be AIME level during the first three rounds -- mostly mid to hard AIME level given that students do have several days to work, but are also challenged for speed. I am always interested in feedback on the problems in order to improve the competition.

While they are difficult to write, my hope is to continue to include a few puzzle problems. I have always enjoyed them more than most other problem types, and they are a little more rare in American mathematics competitions. A competition like this one may simple be a better venue for them than most.


Statistics -- Rounds 1 and 2

Judging from the statistics, the problems have been at an appropriate level. Only six students have answered all ten correctly during the first two rounds. One of those, In Young Cho, has been defeated in Round 2 due to superior time performance by Jeffrey Chen. Congratulations to Cho on a nice performance.

Edit: Justin Kopinsky also correctly answer all 10 problems, making 7 students total. But like Cho, Kopinsky was defeated in Round 2, with Jeremy Hahn solving all five problems in less time. Perhaps Hahn wants to keep the TOC championship at East Chapel Hill (2007 iTest TOC champion Arnav Tripathy graduated from East Chapel Hill).

One surprise to me is that Round 2 problem 4 was the easiest of the round. Out of the 26 students to submit answers, nobody missed it, while five and six students respectively missed problems 1 and 3.

Problem 5 was the hardest on both rounds so far, which is not a big surprise. But I don't believe this was the case last year.

Of the students who submitted problems during the first two rounds, average scores in both rounds were between 17 and 18 points. I didn't really have a goal for that average score, but I feel like these scores suggest that the problems are at a reasonable level of difficulty. It's also probably true that these averages are mildly inflated given that a few students in each round did not submit scores. While in some cases this may reflect that a student simply did not have time to compete or chose to pursue other priorities, it is also likely that a few students did not submit scores in anticipation of defeat, meaning they failed to solve at least one of the problems.

I doubt Round 1 will ever have full participation for this reason, though it's nice to see that over the past couple of years, participation in later rounds has been nearly full.

So, in total, there were five perfect scorers in the "Sweet 16". I'll try to report back as the contest progresses.

Please let us know what you think about the problems in terms of difficulty and topic spread.