MathDB

Two players play the following game: alternatively they write numbers

1

0

in the vertices of an

n

-gon. First player starts the game and wins if after any of his moves there exists a triangle, whose vertices are three consecutive vertices of the

n

-gon, such that the sum of numbers in it's vertices is divisible by

3

. Second player wins if he prevents this. Determine which player has a winning strategy if: a)

n=2019

n=2020

n=2021

3