MathDB

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

111^2

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.

Problem Statement