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2016 LMT
10
2016 LMT Theme #10
2016 LMT Theme #10
Source:
April 11, 2016
Problem Statement
Let
S
=
{
1
,
2
,
3
,
4
,
5
,
6
}
.
S=\{1,2,3,4,5,6\}.
S
=
{
1
,
2
,
3
,
4
,
5
,
6
}
.
Find the number of bijective functions
f
:
S
→
S
f:S\rightarrow S
f
:
S
→
S
for which there exist exactly
6
6
6
bijective functions
g
:
S
→
S
g:S\rightarrow S
g
:
S
→
S
such that
f
(
g
(
x
)
)
=
g
(
f
(
x
)
)
f(g(x))=g(f(x))
f
(
g
(
x
))
=
g
(
f
(
x
))
for all
x
∈
S
x\in S
x
∈
S
.Proposed by Nathan Ramesh
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