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Problems
Contests
National and Regional Contests
China Contests
(China) National High School Mathematics League
2022 China Second Round A2
3
K_500s cover complete graph
K_500s cover complete graph
Source: 2022 China Second Round A2
December 22, 2022
graph theory
combinatorics
Problem Statement
S
=
{
1
,
2
,
.
.
.
,
N
}
S=\{1,2,...,N\}
S
=
{
1
,
2
,
...
,
N
}
.
A
1
,
A
2
,
A
3
,
A
4
⊆
S
A_1,A_2,A_3,A_4\subseteq S
A
1
,
A
2
,
A
3
,
A
4
⊆
S
, each having cardinality
500
500
500
.
∀
x
,
y
∈
S
\forall x,y\in S
∀
x
,
y
∈
S
,
∃
i
∈
{
1
,
2
,
3
,
4
}
\exists i\in\{1,2,3,4\}
∃
i
∈
{
1
,
2
,
3
,
4
}
,
x
,
y
∈
A
i
x,y\in A_i
x
,
y
∈
A
i
. Determine the maximal value of
N
N
N
.
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