Does Brilliant help with AIME preparation?
4 years, 4 months ago
5 months ago
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Brilliant displays problems in a similar fashion as the AIME, not the USAMO. The AIME questions have integral answers between 0 and 999, just like brilliant. The USAMO is purely proofs.
That, of course, depends on one's current difficulty level. The easiest Brilliant questions (Level 1) are much easier than anything one might encounter on the AIME, for instance. In order to write complete and correct solutions for the hardest Level 5 problems, however, one is likely required to demonstrate a degree of mathematics proficiency well above what is typically encountered in an AIME question. This is not to say Level 5 as a whole is "USAMO level"--some questions might be comparable to AIME questions in difficulty, others not.
Problem difficulty, in my view, is not necessarily the most important basis for comparison between USAMO, AIME, and Brilliant questions. I believe an equally important criterion is whether the grading format depends on the student showing a complete and correct solution. In the USAMO, this is required for full credit, so the exposition is a critical aspect of the problem-solving process, just as it is with the William Lowell Putnam Competition.
In this regard, I appreciate that Brilliant problem solvers are occasionally invited to submit their own solutions. This encourages thorough and clear problem analysis, rather than simply furnishing answers based on non-rigorous approaches, such as pattern detection or extrapolating small cases. Occasionally, questions are written in such a way that they may be amenable to computational methods or imposing additional constraints not specified, when an elegant proof of the question as stated is the pedagogical intent. However, reviewing full solutions is a very time-consuming and detail-oriented task (this is one reason why the test format changes from the AIME to the USAMO). There are many more Brilliant members than there are staff to review submitted solutions. If a student wishes to extract the greatest possible benefit from this site, I recommend practicing the writeup of one's own solutions even if one was not invited to do so; comparing these to the featured solutions each week; and where the two substantially differ, investigate those differences and remark on them in the comment section for that problem.
Taehyung, in response to your original question, Brilliant certainly helps with AIME preparation in the way that any high-level problem solving practice will.