MathDB

Players

A

and

B

play the following game on the coordinate plane. Player

A

hides a nut at one of the points with integer coordinates, and player

B

tries to find this hidden nut. In one move

B

can choose three different points with integer coordinates, then

A

tells whether these three points together with the nut's point lie on the same circle or not. Can

B

be guaranteed to find the nut in a finite number of moves?

Problem Statement