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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Maths competitions for undergraduates

What are in the world and in Europe the most important Math competitions for undergraduates? Thank to all who will answer
Extreme_Math
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Problem 20 from Putnam and Beyond

I encountered into problem from book "Putnam and Beyond" which seemed to me quite interesting. However, After a long meditation I can not solve it. Let $x_1, x_2, \dots, x_n, y_1, y_2, \dots, y_m$ be positive integers, $n,m>1$. Assume that…
RFZ
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What is the integer part of $\frac{1}{\sqrt{1}} + \frac{1}{\sqrt{3}} +\cdots + \frac{1}{\sqrt{(2n+1)^2}}$

I tried to solve the following problem. What is the integer part of $$\frac{1}{\sqrt{1}} + \frac{1}{\sqrt{3}} + \cdots + \frac{1}{\sqrt{(2n+1)^2}}=\sum_{k=0}^{2(n^2+n)} \frac 1{\sqrt{2k+1}} ?$$ I tried using some inequalities( by grouping 1,3,5,7 /…
Mahtsolver11
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Squares and Rationalization

I was solving this question, and I'm hitting a wall. If ${1\over{\sqrt{2011+\sqrt{2011^2-1}}}}=\sqrt{m}-\sqrt{n}$, where $m$ and $n$ are positive integers, what is the value of $m+n$? I tried to solve this question with two…
DynamoBlaze
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Solution to this simple problem

The complete question is: A supermarket receives several trucks with boxes of fruit. Each box contain a single type of fruit, which could be mangoes, strawberries, oranges and pears. Each trucks has the same number of boxes. The fruit of which more…
Luis Martínez
  • 59
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Optimal staff selection

There are some staffs N given with certain ratings R(i) based on there performance. Now optimally maximum no. of staff has to be selected to meet certain Standard Rating (R). But Certain provisions are allowed for the staff selection procedure…
Pallab
  • 101
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Koeller rectangle question.

This is a question that appeared on the 2017 CEMC Galois math contest (which took place a few weeks ago): A Koeller rectangle: Is a rectangle $m\times n$, n being a whole number with $m \geq 3$ and $n \geq 3$; has parallel lines on its side…
Daniel H.
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Solving Trigonometric Equation

How to get $ \left(5+\sqrt{6}\right)$ from the expression $$6\sqrt { 3 } \sin { \left( \frac { 2\pi }{ 3 } -\arcsin { \left( \frac { 5\sqrt { 3 } }{ 9 } \right) } \right) } $$ without using calculator for examination purpose?
Pallab
  • 101
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Nonexistence of $f:\mathbb{Z}\to \{1,2,3\}$ with certain properties

Show that there does not exist a function $f:\mathbb{Z}\to \{1,2,3\}$ satisfying $f(x)\neq f(y)$ for all $x,y\in \mathbb{Z}$ such that $|x-y|\in \{2,3,5\}$. Proof: Suppose by contradiction that such function exists and denote it by $f(x)$. Let…
RFZ
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2015 AMC 10A 2015 problem 25

I came across this problem when reviewing previous AMC tens. Let S be a square of side length 1. Two points are chosen independently at random on the sides of S. The probability that the straight-line distance between the points is at least $1/2$…
Tie Fighter
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Find all triplets of natural numbers $(x,y,z)$ that satisfy this equation: $2x^{2}y^{2}+2y^{2}z^{2}+2x^{2}z^{2}-x^{4} -y^{4}-z^{4}=576$

I've tried $(x^{2}-y^{2})^{2}+(y^{2}-z^{2})^{2}+(x^{2}-z^{2})^{2}-x^{4}-y^{4}-z^{4}=-576$ $(x^{2}-y^{2}-z^{2})(x^{2}-y^{2}+z^{2})+(y^{2}-z^{2}-x^{2})(y^{2}-z^{2}+x^{2})+(x^{2}-z^{2}-y^{2})(x^{2}-z^{2}+y^{2})=-576$ I wanted to factor 576 somehow…
user410918
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Minimum and maximum

There are five real numbers $a,b,c,d,e$ such that $$a + b + c + d + e = 7$$$$a^2+b^2+c^2+d^2+e^2 = 10$$ How can we find the maximum and minimum possible values of any one of the numbers ? Source
user6802
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four checkerboard pieces are arranged in a square of sidelength one

This puzzle is from Terrence Tao's book Solving Mathematical Problems: Suppose four checkerboard pieces are arranged in a square of sidelength one. Now suppose that you are allowed to make an unlimited amount of moves, where in each move one takes…
athos
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indian zonal informatics olympiad questions

I stumbled across this question when i was practicing for indian zonal informatic olympiad need some hint to solve this question: Your weekend is ruined because your parents have reminded you of a number of chores to be completed. You can only do…
Aman Gandhi
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