Problem #PRU-35181

Problems Algebra and arithmetic Number theory. Divisibility Division with remainders. Arithmetic of remainders Division with remainder Odd and even numbers Methods Pigeonhole principle Pigeonhole principle (other)
 13–15  4.0

Problem

\(2n\) diplomats sit around a round table. After a break the same \(2n\) diplomats sit around the same table, but this time in a different order.

Prove that there will always be two diplomats with the same number of people sitting between them, both before and after the break.