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Arne has 2n + 1 tickets

Source: Flanders Math Olympiad 2022 p3

December 24, 2022
combinatorics

Problem Statement

Arne has 2n+12n + 1 tickets. Each card has one number on it. One card has the number 00 on it. The natural numbers 1,2,...,n1, 2, . . . , n occur on exactly two cards each. Prove that Arne can arrange cards in a row so that there are exactly mm cards between the two cards with the number mm, for every māˆˆ{1,2,...,n}m \in \{1, 2, . . . , n\}.
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