We are given a set P of points and a set L of straight lines. At the beginning there are 4 points, no three of which are collinear, and L=∅. Two players are taking turns adding one or two lines to L, where each of these lines has to pass through at least two of the points in P. After that all intersection points of the lines in L are added to P, if they are not already part of it. A player wins, if after his turn there are three collinear points from P, which lie on a line that isn’t from L. Find who of the two players has a winning strategy.
Problem
Source: VII International Festival of Young Mathematicians Sozopol 2016, Theme for 10-12 grade
Tags: game strategy, combinatorial geometry