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China Northern Mathematical Olympiad 2017, Problem 4

Source: China Northern Mathematical Olympiad 2017

July 29, 2017
graph theorycombinatorics

Problem Statement

Let QQ be a set of permutations of 1,2,...,1001,2,...,100 such that for all 1≤a,b≤1001\leq a,b \leq 100, aa can be found to the left of bb and adjacent to bb in at most one permutation in QQ. Find the largest possible number of elements in QQ.
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