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Bundeswettbewerb Mathematik 1978 Problem 1.2

Source: Bundeswettbewerb Mathematik Round 1

October 12, 2022
combinatoricsarrangementLine

Problem Statement

A set of n2n^2 counters are labeled with 1,2,…,n1,2,\ldots, n, each label appearing nn times. Can one arrange the counters on a line in such a way that for all x∈{1,2,…,n}x \in \{1,2,\ldots, n\}, between any two successive counters with the label xx there are exactly xx counters (with labels different from xx)?
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