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Kvant 2024
M2786
M2786
Part of
Kvant 2024
Problems
(1)
Coloring game
Source: ARO Regional stage 2024 10.3=11.3
2/2/2024
There are
100
100
100
white points on a circle. Asya and Borya play the following game: they alternate, starting with Asya, coloring a white point in green or blue. Asya wants to obtain as much as possible pairs of adjacent points of distinct colors, while Borya wants these pairs to be as less as possible. What is the maximal number of such pairs Asya can guarantee to obtain, no matter how Borya plays.
combinatorics