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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IWYMIC Team Contest 2017 problem 6

The quadrilateral ABCD is inscribed in a circle with center O. Connect AC and BD intersecting at K.O1 is the circumcenter of triangle ABK and O2 is the circumcenter of triangle CDK. A line l through K intersect the two circumcircles at E and F…
user766994
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For $p\geq5, 1^2+2^2+3^2+...+(p-1)^2$ is divisible by $p$.

I tried to expand this sum using the formula but still can't observe why it can be divided by... I mean eventually, I'll get $(p-1)(2p-1)$ must be divided by $6$, but why?
WWMASK
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Solutions to $2^x=y^2+15$

How to find all solutions to $2^x=y^2+15$? This should be some math Olympiad question. I think the digits in the ones place of $2^x$ are 4 8 6 2 4 so it means $y^2$'s ones place should be 9, 3, 1, 7, 1 where 3 and 7 are impossible so it's 9 and…
WWMASK
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Isosceles triangles + angle chasing

17) Triangle $\bigtriangleup ABC$ and $\bigtriangleup ABD$ are isosceles with $AB=AC=BD$, and BD intersects AC at E(point E is on segment AC and segment BD). If $BD \perp AC$, then $\angle C + \angle D$ is A)$115^{\circ}$ B)$120^{\circ}$…
asdf334
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Find the smallest value of $a+b^3$, where $a$ and $b$ are positive real numbers satisfying $ab=1$

I am unsure as to where to go with this problem. Appreciate anyone who tries to help.
bathris23
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bird going between two moving objects with different speed

Two leopard seals, Snap and Snarl, start 210 meters apart. They swim toward each other at a constant speed of 10 km/h each. Gilly, a gentoo penguin, starts at Snap and swims back and forth between the seals continually until the two seals meet. When…
user526427
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Probability math questions

In a certain Algebra 2 class of 27 students, 11 of them play basketball and 10 of them play baseball. There are 8 students who play both sports. What is the probability that a student chosen randomly from the class plays basketball or baseball?
Tanaja Winnegan
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AoPS 2015-2016 Mock AMC #21, by AlcumusGuy

I was doing a Mock AMC 10 (title) from AoPS (also title). I got really confused on number 21 because solution was bad. Here it is: A positive integer $n$ is called expoprime if for every prime $p$ dividing $n$, there exists a prime number $q$ such…
asdf334
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Solving an exponential expression, given an equation

I am struggling to solve this question, Suppose $$2^x = 6$$, what is the value of $$2^{3x-1}$$ ? I simply do not know where to start. Please note that I am expected to do this with knowledge up to Algebra 1 for this problem was found in an AMC 8 /…
Jamlandia
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Equation with fractional parts

How many solutions has the equation: $\{20 \cdot \{ 13 \cdot\{20 \cdot\{ 13\cdot x\}\} \}\}=x^{2013}$ -? Here $\{z\}=z-[z]$, where $[z]=m \in \mathbb{Z}, \ m \le z < m+1$.
Gordon
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How would we calculate the answer to this simple counting game problem?

I am conscious of the fact that this question is very elementary, but I have no apparent idea as to how one intends to go about it. If someone could kindly provide a layman possessing the soul of myself some mathematical intuition, it would be…
LÜHECCHEgon
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Time & work concept question

If 3 men or 5 women can finish a work in 43 days. Then in how many days 5 men and 6 women together do it ?
Ravi Kadyan
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Suppose that * is an associative operation on a set S.

Suppose that * is an associative operation on a set S. Define $x^n$ to mean $x*x*x*...*x$, $n$ times. (so, for example, $x^3=x*x*x.$) Suppose further that an elements $a$ of S is such that all of $a,a^2,...,a^9$ are different but $a^{10}=a^3$. Then…
nar
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Getting into competition math for an eager to learn high school student

I recently moved countries, and am now in a US school. Previously, I've had a little bit of exposure to competition math, and I did okay, but at this time I wasn't diving very deep into math in general, much less competition math. Today, it's a bit…
Archsys
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SMO 2012 Question 7

Determine the largest even positive integer which cannot be expressed as the sum of two composite odd positive integers. The answer key for this question suggests looking at $n-15$, $n-25$, $n-35$ to see if we can express n as a sum of two…
Hector Lombard
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