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Comment by tlb

5 days ago

I encourage anyone who thinks these are easy high-school problems to try to solve some. They're published (including this year's) at https://www.imo-official.org/problems.aspx. They make my head spin.

22 comments

tlb

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mauriziocalo  4 days ago

Related — these videos give a sense of how someone might actually go about thinking through and solving these kinds of problems:

- A 3Blue1Brown video on a particularly nice and unexpectedly difficult IMO problem (2011 IMO, Q2): https://www.youtube.com/watch?v=M64HUIJFTZM

-- And another similar one (though technically Putnam, not IMO): https://www.youtube.com/watch?v=OkmNXy7er84

- Timothy Gowers (Fields Medalist and IMO perfect scorer) solving this year’s IMO problems in “real time”:

-- Q1: https://www.youtube.com/watch?v=1G1nySyVs2w

-- Q4: https://www.youtube.com/watch?v=O-vp4zGzwIs

bko  4 days ago

I like watching youtube videos solving these problems. They're deceptively simple. I remember reading one:

x+y=1

xy=1

The incredible thing is the explanation uses almost all reasoning steps that I am familiar with from basic algebra, like factoring, quadratic formula, etc. But it just comes together so beautifully. It gives you the impression that if you thought about it long enough, surely you would have come up with the answer, which is obviously wrong, at least in my case.

https://www.youtube.com/watch?v=csS4BjQuhCc

  • Tainnor  4 days ago

    This is slightly tedious to do by hand but there isn't really anything interesting going on in that problem - it's just solving a quadratic equation over the complex numbers.

    • roenxi  4 days ago

      That isn't much of an argument; nothing in math is truly interesting if you take that approach. exp(i\pi)+1=0 could be said to be dis-interesting because it is just rotation on the complex plane. But it is the opposite - it is interesting because it turned out to be rotation on the complex plane but approached from summing infinite series.

      Similarly you can say that solving a quadratic over complex numbers is dis-interesting, but it is actually an interesting puzzle because it is trying its best to pretend it isn't a quadratic. In many ways succeeding, it isn't a quadratic - there is no "2" in it.

      5 replies →

xpressvideoz  5 days ago

I didn't know there were localized versions of the IMO problems. But now that I think of it, having versions of multiple languages is a must to remove the language barrier from the competitors. I guess having that many language versions (I see ~50 languages?) may make keeping the security of the problems considerably harder?

  • dmurray  4 days ago

    The problems are chosen by representatives from all the countries. So every country has someone who knows the full exam before the participants get it. Security is on the honour system, but it seems to mostly work.

  • peteyreplies  3 days ago

    iirc, the IMO system automatically translates the questions into 50 languages, after they are entered in English.

koakuma-chan  4 days ago

How do those compare to leetcode hard problems?

  • kenjackson  4 days ago

    Depends on how hard, but the “average hard” leetcode problem is much easier. These will be more like the ACM ICPC level questions, which I’d put at the “hard hard” leetcode level (also this is a collegiate competition rather than high school, but with broader participation).

kappi  4 days ago

[flagged]

  • yongjik  4 days ago

    All the past IMO problems are known to public and contestants practice on them. If solving an IMO problem is the simple matter of "looking at all the past problems and apply the same pattern," you'd expect human contestants to do a lot better.

    • kappi  4 days ago

      I think you haven't gone thru AMC8, AMC10, AIME competitions. If you are so confident, try giving an unsolved math problem outside the high school math competitions.

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