Problem #PRU-55621

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

13–15 3.0

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).

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