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National and Regional Contests
China Contests
China National Olympiad
2011 China National Olympiad
1
Find the minmum 2011 China national Olmypaid 4
Find the minmum 2011 China national Olmypaid 4
Source:
January 17, 2011
combinatorics proposed
combinatorics
Problem Statement
Let
n
n
n
be an given positive integer, the set
S
=
{
1
,
2
,
⋯
,
n
}
S=\{1,2,\cdots,n\}
S
=
{
1
,
2
,
⋯
,
n
}
.For any nonempty set
A
A
A
and
B
B
B
, find the minimum of
∣
A
Δ
S
∣
+
∣
B
Δ
S
∣
+
∣
C
Δ
S
∣
,
|A\Delta S|+|B\Delta S|+|C\Delta S|,
∣
A
Δ
S
∣
+
∣
B
Δ
S
∣
+
∣
C
Δ
S
∣
,
where
C
=
{
a
+
b
∣
a
∈
A
,
b
∈
B
}
,
X
Δ
Y
=
X
∪
Y
−
X
∩
Y
.
C=\{a+b|a\in A,b\in B\}, X\Delta Y=X\cup Y-X\cap Y.
C
=
{
a
+
b
∣
a
∈
A
,
b
∈
B
}
,
X
Δ
Y
=
X
∪
Y
−
X
∩
Y
.
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