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National and Regional Contests
China Contests
South East Mathematical Olympiad
2009 South East Mathematical Olympiad
5
find │M│
find │M│
Source:
September 18, 2010
combinatorics proposed
combinatorics
Problem Statement
Let
X
=
(
x
1
,
x
2
,
.
.
.
.
.
.
,
x
9
)
X=(x_1,x_2,......,x_9)
X
=
(
x
1
,
x
2
,
......
,
x
9
)
be a permutation of the set
{
1
,
2
,
…
,
9
}
\{1,2,\ldots,9\}
{
1
,
2
,
…
,
9
}
and let
A
A
A
be the set of all such
X
X
X
. For any
X
∈
A
X \in A
X
∈
A
, denote
f
(
X
)
=
x
1
+
2
x
2
+
⋯
+
9
x
9
f(X)=x_1+2x_2+\cdots+9x_9
f
(
X
)
=
x
1
+
2
x
2
+
⋯
+
9
x
9
and
M
=
{
f
(
X
)
∣
X
∈
A
}
M=\{f(X)|X \in A \}
M
=
{
f
(
X
)
∣
X
∈
A
}
. Find
∣
M
∣
|M|
∣
M
∣
. (
∣
S
∣
|S|
∣
S
∣
denotes number of members of the set
S
S
S
.)
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