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4
2009 Combinatorics #4 - Number of Functions
2009 Combinatorics #4 - Number of Functions
Source:
January 7, 2012
function
Problem Statement
How many functions
f
:
f
{
1
,
2
,
3
,
4
,
5
}
⟶
{
1
,
2
,
3
,
4
,
5
}
f : f\{1, 2, 3, 4, 5\}\longrightarrow\{1, 2, 3, 4, 5\}
f
:
f
{
1
,
2
,
3
,
4
,
5
}
⟶
{
1
,
2
,
3
,
4
,
5
}
satisfy
f
(
f
(
x
)
)
=
f
(
x
)
f(f(x)) = f(x)
f
(
f
(
x
))
=
f
(
x
)
for all
x
∈
{
1
,
2
,
3
,
4
,
5
}
x\in\{ 1,2, 3, 4, 5\}
x
∈
{
1
,
2
,
3
,
4
,
5
}
?
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