Math olympiad Definition and 19 Discussions

Mathematics competitions or mathematical olympiads are competitive events where participants sit a mathematics test. These tests may require multiple choice or numeric answers, or a detailed written solution or proof.

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  1. A

    Studying What Should I Be Learning?

    I was browsing the math subreddit on Reddit just a moment ago, and came across someone who was asking for calculus textbooks to give to his precocious eleven year old. That got me thinking: Am I pursuing subjects that are too advanced for my level without trying to pursue rigor and depth? I quit...
  2. T

    Math Olympiad

    How can I go far in the national mathematical olympiad? Do you need to be born with an insane IQ, or born a genius or something like that? Any tips about how I can increase my problem solving skills if it's even possible? Examples of problems you will have to solve in the second round of the...
  3. J

    Math Olympiad problem - Applying induction and the pigeon hole principle

    Ok, so this problem looks like an induction problem to me, so I used that, but I only got as far as the induction hypothesis. The hint says to use the pigeon hole principle. I'm not sure how to use that for this problem.
  4. A

    Abstract algebra question (math olympiad)

    Let G be a non-cyclic group of order pn where p is a prime number. Prove that G has at least p+3 subgroups. Could anyone offer a solution to this problem?
  5. M

    Math Olympiads problem

    Homework Statement f\left(x^{2}+f(y)\right)=y-x^{2} Homework Equations Find all functions f that satisfy the relationship for every real x and y. The Attempt at a Solution is this correct reasoning? for x=0: f(y)=f^{-1}(y) for x>0: \existsxεℝ: x=k^{2}...
  6. M

    Math Olympiads problem that I couldn't do.

    Homework Statement for every (x,y) in ℝ^2: f(x^2+f(y))= y-x^2 Homework Equations Find all functions. The Attempt at a Solution I was wondering if rewriting it as x^2+f(y)=f^-1(y-x^2)?
  7. M

    Frustrated of maths olympiad

    frustrated of maths olympiad! i am from malaysia, where there is lack of training for maths olympiad and the only one out there is far too expensive (arounds hundreds of ringgit) . To compensate this fact, i bought a locally written book about the basics of maths olympiad and it did not do any...
  8. G

    Internat. Math Olympiad exercise. Weird function.

    Homework Statement A friend of mine tried to classify for the IMO a few days ago (he didn't do so well). A problem he had to solve was: f(x + xy + f(y)) = (f(x) + 1/2)(f(x) + 1/2) I didn't really understand what he said later. First he told me to find the values of X and Y for which...
  9. S

    A question from the Russian/Soviet Math Olympiad

    Hey guys. I got a book that has selected problems/questions the from Russian/Soviet Math Olympics. Anyhow, I'm having trouble with a particular question that involves a quartic equation that, up to my knowledge, can't be factored. I was wondering if there are any tips or methods to solve for...
  10. S

    Understanding some of the math Olympiad questions?

    I was looking at some of the questions from various competitions for high schools and colleges and their questions, and I couldn't begin to solve the majority of them. I was looking at and I couldn't follow...
  11. P

    Book for Math Olympiad

    I'm not a natural at math, but I study a lot of it. So I needed something to prepare me for the math olympiads and competitions. Needed comments on this book for preparation: Elementary Number Theory by Gareth Jones...
  12. R

    Your thoughts on the math Olympiad

    I have heard many say that being able to solve Olympiad problems is by no means a prerequisite to becoming a good mathematician, physicist, etc. However, would one benefit from practicing math competition problems if he is older, i.e. undergrad level and on. Would there be any benefit to the...
  13. M

    Math olympiad stuff

    Are there any free, online Math Olympiad resources for studying? These are the high school level math competitions. I'm not looking for past competitions, as much as studying/practice/explanation guides which review material, etc. I welcome any suggestions
  14. Ö

    Turkland maths olympiads

    from my turkish maths olympiads book original question in addition to.. link [Broken] question 19 ^=exponent we are looking for integer solutions (x, y) x^3 - y^3 = 2.(y)^2 + 1 Find how many integer solutions there...
  15. P

    Links to Physics and Maths Olympiads

    Hi, I am in need of very hard physics and maths problems from olympiads best in English/German/Russian. Thanks
  16. F

    Math Olympiad Corner- CMO,USAMO,IMO, and others

    Hello folks, I am quite new to Olympiad level problem solving :smile: , which is why I am considering buying Paul Zeitz's "Art and Craft of Problem Solving". Does anyone have the solutions? I have heard the solutions are in a separate Instructor's Manual, does anyone know how someone can get...
  17. T

    Math olympiad problem

    i have 69 distinct positive whole numbers between 1 and 100. i pick out 4 integers a,b,c,d. prove that i can always pick out 4 integers such that a+b+c=d. can this always hold true with 68 positive integers?
  18. G

    Maths Olympiad Problem

    The following is a problem I got in a Maths Olympiad, I had to solve it without a calculator, although I couldn't solve it: sin 1 + sin 2 + sin 3 + ... + sin 90 If anyone could show me how to solve this I would really appreciate it.
  19. D

    Hard probability problem (1973 British Math Olympiad #6)

    I'm trying to pull some old Olympiad questions for some students, but I can't get a handle on this one. I'd really like to include it, though. In answering general knowledge questions (framed so that each question is answered yes or no), the teacher's probability of being correct is A and a...