Math olympiad Definition and 26 Threads

Hi! I am 12, and will be a 13 in 9th grade ( I skipped 6th grade). I have a curiosity for mathematics and have started preparing to take the AMC 10 and 12 exams. I enjoy solving the ingeniously crafted problems, as I share the sentiment of many math competitors of not being challenged by the...

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...

and the associated movie staring Asa Butterfield as Nathan Ellis (Daniel Lightwing in the documentary) You can find the movie on Amazon Prime Video as a Prime movie.

Im just looking for someone to explain me some problems

Homework Statement ok here is another problem that wrecked me in todays olympiad find smallest integer n such that 5 (32 + 22)(34 + 24)(38 + 28)...(32n + 22n) > 9256 Homework EquationsThe Attempt at a Solution ok once again how am i supposed to start does writing 3 = 2+1 help? i don't see...

Homework Statement this problem came out in the math olympiad i took today and i got completely wrecked by this consider the following equation where m and n are positive integers: 3m + 3n - 8m - 4n! = 680 determine the sum all possible values of m: Homework Equations not sure which The...

<Moderator's note: moved from a technical forum, so homework template missing.> so this is the question. i want to know if there is a solution without using calculus maybe trig substitution maybe other methods? i tried trig substitition i let u = √2 cosx and v be sinx am i on the right track

so this is the question: let a and b be real numbers such that 0<a<b. Suppose that a3 = 3a -1 and b3 = 3b -1. Find the value of b2 -a. initially my line of thinking was that just solve the equation x3 - 3x +1 = 0 and take the roots which are more than 0 and then after that i got stuck ok that...

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...

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.

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?

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}...

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)?

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...

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...

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...

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 http://books.google.com/books?id=B3EYPeKViAwC&printsec=frontcover&dq=Problem+Solving and I couldn't follow...

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...

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...

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

from my turkish maths olympiads book original question in addition to.. link http://www.akdeniz.edu.tr/fenedebiyat/math/olimpiyat/2006a.pdf 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 are to...

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

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...

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?

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.

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...