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Problems
Contests
National and Regional Contests
Korea Contests
Korea Junior Mathematics Olympiad
2007 Korea Junior Math Olympiad
6
6
Part of
2007 Korea Junior Math Olympiad
Problems
(1)
f(f(x)) = x, |f(x) - x| \ge 2, f : T\to ={1,2,...,10}
Source: KJMO 2007 p6
5/2/2019
Let
T
=
{
1
,
2
,
.
.
.
,
10
}
T = \{1,2,...,10\}
T
=
{
1
,
2
,
...
,
10
}
. Find the number of bijective functions
f
:
T
→
T
f : T\to T
f
:
T
→
T
that satis es the following for all
x
∈
T
x \in T
x
∈
T
:
f
(
f
(
x
)
)
=
x
f(f(x)) = x
f
(
f
(
x
))
=
x
∣
f
(
x
)
−
x
∣
≥
2
|f(x) - x| \ge 2
∣
f
(
x
)
−
x
∣
≥
2
algebra
bijective function
functional equation
function