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I am looking for word problems that can be tackled by subjects like category theory, commutative algebra, nonlinear algebra, algebraic geometry etc.

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  • $\begingroup$ No, math olympiads only assume somewhat advanced high school methods (plus standard combinatorial trickery). No advanced topics (on purpose ! it should be accessible to gifted high school students). $\endgroup$ Oct 27, 2021 at 10:00
  • $\begingroup$ Yes, and I was hoping there are word problems that are challenging for gifted high school students but quite trivial for practitioners of modern math. Any examples? $\endgroup$
    – Cel
    Oct 27, 2021 at 10:04
  • $\begingroup$ No, none that I've ever seen.. $\endgroup$ Oct 27, 2021 at 10:09
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    $\begingroup$ Actually, there are some examples about integer solutions of $y^2=x^3+m$, where completely elementary methods suffice, for some $m$, but which are obvious if you know about Mordell curves. But they are usually not olympiad questions. $\endgroup$ Oct 27, 2021 at 10:18
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    $\begingroup$ I heard that the idea for IMO 2017 P6 came from a book of algebraic geometry, and that the IMO 2008 P5 was originally a question about a hypercube. And I know at least a few examples of olympiad problems where I was quite stumped as a high-schooled but I solved it effortlessly with two more years of math general education and overall practise. See also math.stackexchange.com/questions/4264555/… for a nonelementary approach to a question “harder” than a N7 of an imo shortlist. $\endgroup$
    – Aphelli
    Oct 27, 2021 at 10:31

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