Two players A and B play the following game:
A chooses a point, with integer coordinates, on the plane and colors it green, then B chooses 10 points of integer coordinates, not yet colored, and colors them yellow. The game always continues with the same rules; A and B choose one and ten uncolored points and color them green and yellow, respectively.
a. The objective of A is to achieve 1112 green points that are the intersections of 111 horizontal lines and 111 vertical lines (parallel to the coordinate axes). B's goal is to stop him. Determine which of the two players has a strategy that ensures you achieve your goal.
b. The objective of A is to achieve 4 green points that are the vertices of a square with sides parallel to the coordinate axes. B's goal is to stop him. Determine which of the two players has a strategy that will ensure that they achieve their goal. combinatoricsColoringgamecombinatorial geometry