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

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Found problems: 2

2017 Vietnamese Southern Summer School contest, Problem 4
In a square board of size 1001 x 1001, we color some $m$ cells in such a way that: i. Of any two cells that share an edge, at least one is colored. ii. Of any 6 consecutive cells in a column or a row, at least 2 consecutive ones are colored. Determine the smallest possible value of $m$.
combinatorics minimize square grid

2020 USOMO, 1
Let $ABC$ be a fixed acute triangle inscribed in a circle $\omega$ with center $O$. A variable point $X$ is chosen on minor arc $AB$ of $\omega$, and segments $CX$ and $AB$ meet at $D$. Denote by $O_1$ and $O_2$ the circumcenters of triangles $ADX$ and $BDX$, respectively. Determine all points $X$ for which the area of triangle $OO_1O_2$ is minimized. [i]Proposed by Zuming Feng[/i]
olympiad geometry geometry area of a triangle minimize Pythagorean theorem angle chasing complex numbers coordinate method cyclic quadrilaterals law of sines modular arithmetic radical axis similar triangles