Simon Marais 2020 was held on October 10, which is long ago. Due to many coincidences I and my affiliated school missed the chance to take part in the competition. At the same time I didn't have the chance to review the questions until now, so this is a very brief and irresponsible review on the exam this year.
A1: closed curve and stupid pigeonhole.
A2: clear once you figure out how the piling interacts each other, especially when $k \mid n$ or not.
A3: nicely formulated question, although the solution reduces drastically to a bound instead of some fancy sets. The beauty of the solution lies on fact that this sum can be optimized greedily. Locally this is simply year 1 differentiation, and you will reckon that a specific geometric series will do the job.
A4: yeah it sounds fancy and intimidating, but someone may as well brute force all the way with coordinate geometry techniques. I do not see that to be more difficult than IMO-level questions that can also be defeated using co-geom brute force techniques.
B1: this is more like assignment question...not even interested to do that. Question of such depth should not even appear in these contests.
B2: oh unit fractions. This is also a nicely written question. The solution lies on the fact that you can order arrangements in $S_k$ such that raising the sum means a descent in order, which means that it does not go forever.
B3: this is the kind of question that I do not like, where you either know one trick that you easily solves the question, or you have no chance at all. We have had enough cat and mouse questions.
B4: Again, possible (a) and impossible (b).
We see that the difficulty has been pretty consistent in the past years, but we have yet to observe more abstractly formulated questions as in the Putnam exam. Questions that can be formulated rather easily, but the solution requires further thoughts. Again I strongly recommend the removal of Q1, and extend the exam into 6 questions with a more approachable difficulty ladder.
Oh well, I have had a nice afternoon solving these problems.
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