Problem #PRU-55621

Problems Calculus Real numbers Integer and fractional parts. Archimedean property Methods Pigeonhole principle Pigeonhole principle (angles and lengths)

Problem

A rectangular billiard with sides 1 and \(\sqrt {2}\) is given. From its angle at an angle of \(45 ^\circ\) to the side a ball is released. Will it ever get into one of the pockets? (The pockets are in the corners of the billiard table).