This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 79

2021 Kyiv Mathematical Festival, 2
Tags: Kyiv mathematical festival , combinatorics
In 11 cells of a square grid there live hedgehogs. Every hedgehog divides the number of hedgehogs in its row by the number of hedgehogs in its column. Is it possible that all the hedgehogs get distinct numbers? (V.Brayman)

2016 Kyiv Mathematical Festival, P3
Tags: Kyiv mathematical festival , inequalities
1) Let $a,b,c\ge0$ and $ab+bc+ca=2.$ Prove that \[\frac{ab}{c+1}+\frac{bc}{a+1}+\frac{ca}{b+1}+2(a+b+c)\ge6.\] 2) Let $a,b,c\ge0$ and $ab+bc+ca=3.$ Prove that \[\frac{ab}{c+1}+\frac{bc}{a+1}+\frac{ca}{b+1}\ge\frac{3}{2}.\]

2018 Kyiv Mathematical Festival, 5
Tags: Kyiv mathematical festival , combinatorics , geometry , game strategy
A circle is divided by $2019$ points into equal parts. Two players delete these points in turns. A player wins, if after his turn it is possible to draw a diameter of the circle such that there are no undeleted points on one side of it. Which player has a winning strategy?

2009 Kyiv Mathematical Festival, 1
Tags: trigonometry , equation , Trigonometric Equations , algebra , Kyiv mathematical festival
Solve the equation $\big(2cos(x-\frac{\pi}{4})+tgx\big)^3=54 sin^2x$, $x\in \big[0,\frac{\pi}{2}\big)$