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National and Regional Contests
India Contests
India LIMIT
2020 LIMIT
2020 LIMIT Category 2
1
Number of involutions
Number of involutions
Source: LIMIT 2020 Cat 2 Obj P1
May 25, 2020
limit
functions
involution
counting
Problem Statement
Find the number of
f
:
{
1
,
…
,
5
}
→
{
1
,
…
,
5
}
f:\{1,\ldots, 5\}\to \{1,\ldots, 5\}
f
:
{
1
,
…
,
5
}
→
{
1
,
…
,
5
}
such that
f
(
f
(
x
)
)
=
x
f(f(x))=x
f
(
f
(
x
))
=
x
(A)
26
26
26
(B)
41
41
41
(C)
120
120
120
(D)
60
60
60
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