MathDB

4

Part of 2021 China Second Round A1

Problems(1)

Coloring Points on a circle

Source: 2021 China Second Round Olympiad(B) P4

3/6/2022
There are 100 points on a circle that are about to be colored in two colors: red or blue. Find the largest number kk such that no matter how I select and color kk points, you can always color the remaining 100āˆ’k100-k points such that you can connect 50 pairs of points of the same color with lines in a way such that no two lines intersect.
combinatorics