Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [contest-math]

For questions about mathematics competitions or the questions that typically appear in math competitions. Provide enough information about the source to confirm the question doesn't come from a live contest.

This tag is intended for

  1. Questions from mathematics competitions.
  2. Inquiries about alternative proofs for problems that are from math contests.
  3. Questions that have been inspired by a contest problem, including practice problems.
  4. Questions requesting advice on competing in contests.

See this list of mathematics competitions to get an idea of the types of questions this tag is for.

Mathematics StackExchange has a policy on questions from current competitions. Questions from ongoing competitions will be locked and temporarily deleted until the end of the contest. It is a good idea to include information about a contest, such as a link to the contest webpage.

9758 questions
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$f(\frac{x^2}{x+1}) = p(x)$

Does there exist a rational function $f$ and a polynomial in $\mathbb{R}[x]$ so that: $$f(\frac{x^2}{x+1}) = p(x)$$
mtheorylord
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An olympiad question

I came across a question ( mentioned below ) which is from a Mathematical Olympiad. It says, If $m $ and $n $ are positive integers such that $n + (n + 1) + (n + 2) +...+ (n + m) = 1000 $ then how many $(m, n)$ pairs exists ?
user 493905
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Sum of Digits of 4th Powers

Question: Find the sum of digits of the $1^4 +2^4 + ...... + 25^4$ I can't seem to find a way to solve this question without using brute force. Is there a simpler way to solve this question?
Hector Lombard
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Cancellation law on a commutative and associative binary operation on a set $S$

I need to Show: Let$*$ be a commutative and associative binary operation on a set $S$. Assume that for every $x$ and $y$ in $S$, there exists $z$ in $S$ such that $x*z=y$.(This z may depend on $x$ and $y$.) Show that if $a,b,c$ are in $S$ and ac=bc,…
user614287
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Question in My Son's Math Training Worksheet that Has Me Completely Baffled

I am not sure what title to put as the question really has both me and my son confused. It says this: "If PLUS equals 68, what does MINUS equal?" and the choices are: A. 102 B. 76 C. 120 D. 46 and the answer provided in the answer key was…
RC Wong
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Nigerian Olympiad 2017 Second Round,Question 3-Logic

A student has seven pieces of paper. She chooses some of them and cuts each of them into seven pieces. In the sequel, he chooses some of the pieces and cuts each of them into seven pieces. She continues this procedure many times with the pieces she…
Temidire Adesiji
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COMC Problem of the Week Problem

Problem of the Week- Week 5 of COMC Can anyone please tell me if my solution is correct. So, I divide the equation by "$a_n$" in the numerator and denominator ($a_n$ cannot be zero). I get: $a_{n+1} =$ 1 / (n + 1/(a_n)) Using this new…
Alan Tam
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Fraction Word Problem

A computer virus destroys computer memory. On the first day, it destroyed half of this memory. On the second day, it destroyed a third of the memory remaining after the first day; on the 3rd day, it destroyed a fourth of the memory remaining after…
Vyas
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How many 5-digit numbers are multiples of 5 and 8?

Please help me with this question that I have been stuck on. It is an APMOPS question.
hoanggggg
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PAMO G Qualification Exam Question

ABCD is rectangular court with AB = 50m and BC = 30m. Four girls stand at different positions in that court so that the distance between the two girls next to each other is maximised. What is this distance? A. 46m B. 34m C. 26 + (2/3)m D. 20m E.…
user346756
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Been trying to work this out for a while, please help me.

It is known that among any three students in a class, two of them are friends. The total number of students is $25$ prove that their is a student with at least $12$ friends. How do I work this out?
Hunter
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Finding Sum of all Distict number whose LCM is N

The problem was : For a given positive integer N, what is the maximum sum of distinct numbers such that the Least Common Multiple of all these numbers is N. for n=1) Only possible number is 1, so the maximum sum of distinct numbers is exactly 1.…
Syed Shibli
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How do you calculate this

I know it converges, but i need to know the sum of this, i don't know the expression because i'm not English... I need it for my homework and I don't know how to do it, so please if somebody knows how to, I would be glad if he could post it here.
Majky28
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An olympiad number theory problem

i'am struggling to solve this problem can you help me please Let $p$ be a prime number such that there exists two positive integers $m,n$ s.t $$p^2=\frac{(m^2+n^2)}{2}$$ Prove that there exists a positive integer a such that : $$2p-m-n=a^2 \text{ or…
ayoub adnane
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AMC Question 28

A quadrilateral with sides 15, 15, 15 and 20 is drawn with each vertex on a circle. Around this circle, a square is drawn, with each side tangent to the circle. What is the area, in square units, of this square? Someone suggested to me to use…
uservg
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