MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Harvard-MIT Mathematics Tournament
2021 Harvard-MIT Mathematics Tournament.
4
2021 Combo #4: Counting Functions
2021 Combo #4: Counting Functions
Source:
May 30, 2021
Combo
function
Problem Statement
Let
S
=
{
1
,
2
,
…
,
9
}
.
S = \{1, 2, \dots, 9\}.
S
=
{
1
,
2
,
…
,
9
}
.
Compute the number of functions
f
:
S
→
S
f : S \rightarrow S
f
:
S
→
S
such that, for all
s
∈
S
,
f
(
f
(
f
(
s
)
)
)
=
s
s \in S, f(f(f(s))) =s
s
∈
S
,
f
(
f
(
f
(
s
)))
=
s
and
f
(
s
)
−
s
f(s) - s
f
(
s
)
−
s
is not divisible by
3
3
3
.
Back to Problems
View on AoPS