## Saturday, 13 October 2018

### Thoughts on Simon Marais 2018

This is the second time I am involved in this competition...and again of course, not in the role of contestants. Here are some short comments.

A1. Very good -- it is not that kind of idiotic question like last year. However I read the question as "find n for one can tile a n*n square with non-congruent dominant rectangles". This is another question, of difficulty in another dimension.

The main problem is still very easy. You can either look for family of solutions mod 3, or family of solutions mod 4. Both can be easily found.

Difficulty rating: Easy [2/10]

A2. A very nice setup. Once you realize everything can be scaled you can lower the dimension and the rest is simple by drawing some graphs.

Difficuly rating: Easy [3/10]

A3. Not very hard but tricky to write down a precise proof since the DE does not seem to have a short analytical solution. One would like to estimate and bound the solution curve by extending bit by bit on the interval 0
Difficulty rating: Moderately easy [4/10]

A4. The recurrence relation is easy to obtain, while the sum is hard to get. Partial credit is still better than nothing for an A4 even if this is not Putnam.

Difficulty rating: Hard [7/10]

B1. Oh come on standard linear algebra. One replaces min by max and it could look a bit more intimidating...

Difficulty rating: Super easy [2/10]

B2. High school surd exercise? One can make simpler and much stronger claims using density.

Difficulty rating: Super easy [2/10]

B3. The speed of the two slower spiders is a strong hint on how you should use them. Otherwise this is really a non-trivial claim.

Difficulty rating: Moderately hard [6/10]

B4. Comparing with the one last year, the object of interest this year seemed...not very useful at all. It's just like an ad hoc matrix just for fun...whatever.

If you looked for the case m=2,3,4 then you should be able to see through what's happening with m=5, and more importantly why is it a mess for m>5. Easy partial credit, but who dares to take the open problem?

Difficulty rating: Moderately easy [4/10] for partial credit + ???

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Much harder than last year, and it is closer to what it should have been. The spreading of part A is desirable, while that for part B is dreadful. Would really appreciate if they decide to add more questions to widen the breath and difficulty spectrum.