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Problem 1 of Finals - Game strategy with lines and points

Source: VII International Festival of Young Mathematicians Sozopol 2016, Theme for 10-12 grade

September 19, 2019
game strategycombinatorial geometry

Problem Statement

We are given a set PP of points and a set LL of straight lines. At the beginning there are 4 points, no three of which are collinear, and L=∅L=\emptyset . Two players are taking turns adding one or two lines to LL, where each of these lines has to pass through at least two of the points in PP. After that all intersection points of the lines in LL are added to PP, if they are not already part of it. A player wins, if after his turn there are three collinear points from PP, which lie on a line that isn’t from LL. Find who of the two players has a winning strategy.
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