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.

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What is Stewart's Theorem?

What is Stewart's Theorem? I know it has something to do with triangles. I saw it being mentioned in a MathCounts practice.
PotatoLatte
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A very different, difficult geometry problem that need to be helped-

The problem: In $\triangle PQR$, $ST$ is the perpendicular bisector of $PR$, and $PS$ is the bisector of $\angle QPR$ and the point $S$ lies on $QR$. If $|QS|=9$ and $|SR|=7$ and $|PR|=x/y$, where $x$ and $y$ are co-primes, then what is $x+y$? I…
Curious learner
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Topic for a math paper competiton

I'm looking for a topic for a national Math Paper competiton for High School students. The problem is that in the paper I have to study some unsolved before problem. My main interest is mathematical analysis but I know it's difficult to study…
TheRlee
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What is the total of all the possible final scores that cannot be achieved in this game?

In a new game called Nooseball, you can only score points 2 ways. You can score 7 points for a "touchdown," and 3 points for a "field goal." What is the total of all the possible final scores that cannot be achieved in this game? I'm having a…
space
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area or volume (amc)?

A thin piece of wood of uniform density in the shape of an equilateral triangle with side length $3$ inches weighs $12$ ounces. A second piece of the same type of wood, with the same thickness, also in the shape of an equilateral triangle, has side…
space
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Trying to generalize a contest-math problem.

In a regular (a) pentagon (b) hexagon all diagonals are drawn. Initially each vertex and each point of intersection of the diagonals is labeled by the number $1.$ In one step it is permitted to change the signs of all numbers of a side or…
Student
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Number is simultaneously a sum of $2,3,\dots,n$ squares of natural numbers

I have encountered into very nice problem. Prove that for any positive integer $n\geqslant 2$ there is a positive integer $m$ that can be written simultaneously as a sum of $2, \ 3, \dots, \ n$ squares of nonzero integers. My solution: I have tried…
RFZ
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$a+b+c=2,\ a+b^2+c^2=12$, what is the maximum value of c?

Given that $a+b+c=2$ and $a+b^2+c^2=12$, what is the maximum value of c? I have struggled with this problem for a few hours but couldn't solve. How should I solve it?
abouttostart
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probability( central limit theory)

A seed manufacturer sells seeds in packets of 50. Assume that each seed germinates with probability .99 independently of all the others.The manufacturer promises to replace, at no cost to the buyer, any packet with 3 or more seeds that do not…
Alkha
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Probably an average algebra question, but I need help with the interpretation.

For the function f, f(2(x)) = x^2+x−2 for all real numbers x. Let a and b be the sum and product, respectively, of the roots of the equation f((x)/2) = 4. Find a + b.
bigfattyboi
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About International Mathematics Competition (IMC)

Can someone suggest me a book (or books), to practice for International Mathematics Competition (IMC)? Also, how much does the participation to IMC cost?
Sotiris Z.
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Googol and Googolplex Question(Australian Maths Competition)

Not sure if I should ask this here, but I've tried other places with no success. I've pretty lost with this question.. Question: One googol is the number G=10¹⁰⁰, and one googolplex is 10ᴳ. Let n be the largest whole number for which nⁿ<10ᴳ. How…
Jonathan
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Basic proof techniques for math Olympiad

I am very very interested in mathematical proof. I have learned basic proof techniques such as contradiction, mathematical induction, inclusion-exclusion etc. So, I want a list of mathematical proofs which must be basic to advanced.…
SKL
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AMC 10 question

Question In how many ways can $345$ be written as the sum of an increasing sequence of two or more consecutive positive integers? Answer Factor $345=3 \times 5 \times 23$. Suppose we take an odd number $k$ of consecutive integers, centered on $m$.…
Math
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determine the largest car tyres lifespan

A certain brand of car tyres last 450 km on a front wheel or 600 km on a rear wheel. By swapping the front and rear tyres, what is the largest distance in km that can be travelled using this set of four tyres?
Epa
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