Problem #PRU-98267

Problems Methods Pigeonhole principle (finite number of poits, lines etc.) Pigeonhole principle Proof by contradiction

Problem

Some points with integer coordinates are marked on a plane. It is known that no four of the marked points lie on the same circumference of a circle (that is, no circle passes through four of them). Prove that there exists a circle of radius \(1995\) whose circumference contains none of the marked points.