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CIIM
2022 CIIM
4
4
Part of
2022 CIIM
Problems
(1)
Find the number of permutations!
Source: CIIM 2022 - Problem 4
9/19/2023
Given a positive integer
n
n
n
, determine how many permutations
σ
\sigma
σ
of the set
{
1
,
2
,
…
,
2022
n
}
\{1, 2, \ldots , 2022n\}
{
1
,
2
,
…
,
2022
n
}
have the following property: for each
i
∈
{
1
,
2
,
…
,
2021
n
+
1
}
i \in \{1, 2, \ldots , 2021n + 1\}
i
∈
{
1
,
2
,
…
,
2021
n
+
1
}
, the number
σ
(
i
)
+
σ
(
i
+
1
)
+
⋯
+
σ
(
i
+
n
−
1
)
\sigma(i) + \sigma(i + 1) + \cdots + \sigma(i + n - 1)
σ
(
i
)
+
σ
(
i
+
1
)
+
⋯
+
σ
(
i
+
n
−
1
)
is a multiple of
n
n
n
.
permutations
counting
number theory
Divisibility