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That's another thing that irks me about mathematics competitions as you alluded to in this post; the style of the test greatly influences the score of a participant. If the competitions were focused purely on mathematical skill, then theoretically each participant would do just as well regardless of format, but this is not the case.Yes so true on the competitions. They can never delve deeply into some problem and instead rely on the student noticing some insight above and beyond what they learned in traditional math courses. I took the MAA once and was lucky to get a single problem right.

My friend on the other was quite talented and became an MAA champion and was on a team that competed internationally with England and Russia. They failed miserably mostly due to the test structure. The US MAA was a multiple choice affair where you could strike out some non-answers and focus on the reduced set and make an educated guess. The international test was fill in the blanks for which the English and Russian teams routinely tested on.

The English in particular have the Tripos tests which students study for like crazy often using experienced tutor coaches. These tests dictated where in the hierarchy of academia you stood. The math tripos was the oldest of these tests.

https://en.wikipedia.org/wiki/Mathematical_Tripos

I think it was GH Hardy who lobbied for changes in these tests as he felt that had held England back a hundred years or more in mathematics as compared to Europe. Basically the English were focused on appplied math (tripos type problems) and Europe was into rigorous proofs and pure math.

https://en.wikipedia.org/wiki/G._H._Hardy

Thanks for the links for the reading, I found them quite interesting.