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China Team Selection Test
2018 China Team Selection Test
4
A Set Addition Problem
A Set Addition Problem
Source: 2018 China TST 3 Day 2 Problem 4
March 27, 2018
combinatorics
set theory
Problem Statement
Suppose
A
1
,
A
2
,
⋯
,
A
n
⊆
{
1
,
2
,
⋯
,
2018
}
A_1,A_2,\cdots ,A_n \subseteq \left \{ 1,2,\cdots ,2018 \right \}
A
1
,
A
2
,
⋯
,
A
n
⊆
{
1
,
2
,
⋯
,
2018
}
and
∣
A
i
∣
=
2
,
i
=
1
,
2
,
⋯
,
n
\left | A_i \right |=2, i=1,2,\cdots ,n
∣
A
i
∣
=
2
,
i
=
1
,
2
,
⋯
,
n
, satisfying that
A
i
+
A
j
,
1
≤
i
≤
j
≤
n
,
A_i + A_j, \; 1 \le i \le j \le n ,
A
i
+
A
j
,
1
≤
i
≤
j
≤
n
,
are distinct from each other.
A
+
B
=
{
a
+
b
∣
a
∈
A
,
b
∈
B
}
A + B = \left \{ a+b|a\in A,\,b\in B \right \}
A
+
B
=
{
a
+
b
∣
a
∈
A
,
b
∈
B
}
. Determine the maximal value of
n
n
n
.
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