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When I participated in the 2019 John Hopkins Math Tournament, the team round consisted of two separate topics, 40 minutes per round, and 3 people per team. My team suffered on the topology round. Only one team managed to get through more than a third of the round, and that was because one of their team members had taken topology before.

Now that I'm in college and actually taking topology, I decided to revisit the round. The questions are easy*, but 40 minutes for 13 problems, some of which contain multiple parts or subproblems, is just not enough time. I'm sure that even my professor would struggle to scribble down an answer for each question in reasonable detail within the time limit. With that being said, my specific question is as such: How long should the team round be to ensure that students with knowledge of set theory, but little to no prior knowledge of topology, would be able to solve at least half of the questions?

2019 JHMT Topology Round

*In the sense that they serve as normal difficulty homework problems.

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    $\begingroup$ Competitions are not necessarily intended for everyone to solve most or all of the problems. If there's a chance that multiple teams answer them all, then you can't identify a winner. It makes sense to be skewed in the other direction and zero out most teams in order to easily identify one champion (the number and standing of non-winners is not relevant). Consider the Putnam Competition: I got half credit on one problem once and got an award for that at my school. $\endgroup$ Sep 15 '20 at 7:03
  • $\begingroup$ @DanielR.Collins Putnam has a high range, with the median score being 0-1 and someone scoring >90 points every year. This competition wouldn't if you exclude the outlier team that had a member that already knew topology. $\endgroup$ Sep 15 '20 at 11:14
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    $\begingroup$ Somewhat orthogonal to what you asked, I wonder to what extent this is intended to reward students who have had exposure to more advanced topics in mathematics vs. to reward students who have a highly developed level of mathematical maturity? If the latter, then the questions are very inappropriate in my opinion. $\endgroup$ Sep 15 '20 at 12:48
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    $\begingroup$ Curiously, less than 10 minutes after making the comment above, I got an upvote on this answer. $\endgroup$ Sep 15 '20 at 13:07
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    $\begingroup$ @DanielR.Collins I was going to say the same. It's the reason that tests like the SAT are useless to find the best-of-the-best: there are too many perfect scores. In order to select the winner of the competition, you need to be able to distinguish the top scorer. Maybe your comment should be an answer. $\endgroup$
    – shoover
    Sep 16 '20 at 20:34

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