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Existence of a sector

Source: 2022 Thailand MO Day 1 P3

June 15, 2022
combinatorics

Problem Statement

Let Ω\Omega be a circle in a plane. 20222022 pink points and 25652565 blue points are placed inside Ω\Omega such that no point has two colors and no two points are collinear with the center of Ω\Omega. Prove that there exists a sector of Ω\Omega such that the angle at the center is acute and the number of blue points inside the sector is greater than the number of pink points by exactly 100100. (Note: such sector may contain no pink points.)
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