MathDB

In a game, the first player paints a point on the plane red; the second player paints 10 uncoloured points on the plane green; then the first player paints an uncoloured point on the plane red; the second player paints 10 uncoloured points on the plane green; and so on. The first player wins if there are three red points which form an equilateral triangle. Can the second player prevent the first player from winning?
(A Kanel)

Problem Statement