Problem

Source: 2018 China TST 3 Day 2 Problem 4

Tags: combinatorics, set theory



Suppose $A_1,A_2,\cdots ,A_n \subseteq \left \{ 1,2,\cdots ,2018 \right \}$ and $\left | A_i \right |=2, i=1,2,\cdots ,n$, satisfying that $$A_i + A_j, \; 1 \le i \le j \le n ,$$are distinct from each other. $A + B = \left \{ a+b|a\in A,\,b\in B \right \}$. Determine the maximal value of $n$.