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For each k, there are exactly k numbers between the two k

Source: IMO LongList 1982 - P52

May 16, 2011
invariantmodular arithmeticcombinatorics proposedcombinatorics

Problem Statement

We are given 2n2n natural numbers 1,1,2,2,3,3,…,n−1,n−1,n,n.1, 1, 2, 2, 3, 3, \ldots, n - 1, n - 1, n, n. Find all nn for which these numbers can be arranged in a row such that for each k≤nk \leq n, there are exactly kk numbers between the two numbers kk.
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