Given a sequence $1,1,2,2,3,3,\ldots,1986,1986$, determine, with proof, if we can rearrange the sequence so that for any integer $1\le k \le 1986$ there are exactly $k$ numbers between the two “$k$”s.
Problem
Source: China Mathematical Olympiad 1986 problem5
Tags: combinatorics unsolved, combinatorics