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any pair of (1,2),(2,4),...,(1000,2000) contains 1 from set {1,2,...,2000}

Source: 2015 Belarus TST 2.1

November 5, 2020
combinatorics

Problem Statement

N numbers are marked in the set {1,2,...,2000}\{1,2,...,2000\} so that any pair of the numbers (1,2),(2,4),...,(1000,2000)(1,2),(2,4),...,(1000,2000) contains at least one marked number. Find the least possible value of NN.
I.Gorodnin
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