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Argentina Iberoamerican TST
2024 Argentina IberoAmerican TST
Problem 4
Two permutations
Two permutations
Source: Argentina IberoAmerican TST 2024 P4
August 9, 2024
combinatorics
Problem Statement
Determine all natural numbers
n
≥
2
n \ge 2
n
≥
2
with the property that there are two permutations
(
a
1
,
a
2
,
.
.
.
,
a
n
)
(a_1, a_2,... , a_n)
(
a
1
,
a
2
,
...
,
a
n
)
and
(
b
1
,
b
2
,
.
.
.
,
b
n
)
(b_1, b_2,... , b_n)
(
b
1
,
b
2
,
...
,
b
n
)
of the numbers
1
,
2
,
.
.
.
,
n
1, 2,..., n
1
,
2
,
...
,
n
such that
(
a
1
+
b
1
,
a
2
+
b
2
,
.
.
.
,
a
n
+
b
n
)
(a_1 + b_1, a_2 +b_2,..., a_n + b_n)
(
a
1
+
b
1
,
a
2
+
b
2
,
...
,
a
n
+
b
n
)
are consecutive natural numbers.
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