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Vietnam TST 2016 Problem 2

Source: Vietnam TST 2016

March 25, 2016
combinatorics

Problem Statement

Let AA be a set contains 20002000 distinct integers and BB be a set contains 20162016 distinct integers. KK is the numbers of pairs (m,n)(m,n) satisfying {m∈A,n∈B∣m−n∣≤1000 \begin{cases} m\in A, n\in B\\ |m-n|\leq 1000 \end{cases} Find the maximum value of KK
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