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Problems
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International Contests
Pan-African Shortlist
2017 Pan-African Shortlist
I4
I4
Part of
2017 Pan-African Shortlist
Problems
(1)
PAMO 2017 Shortlst: Sum of maxima of adjacent pairs in permutation
Source: 2017 Pan-African Shortlist - I4
5/5/2019
Find the maximum and minimum of the expression
max
(
a
1
,
a
2
)
+
max
(
a
2
,
a
3
)
,
+
⋯
+
max
(
a
n
−
1
,
a
n
)
+
max
(
a
n
,
a
1
)
,
\max(a_1, a_2) + \max(a_2, a_3), + \dots + \max(a_{n-1}, a_n) + \max(a_n, a_1),
max
(
a
1
,
a
2
)
+
max
(
a
2
,
a
3
)
,
+
⋯
+
max
(
a
n
−
1
,
a
n
)
+
max
(
a
n
,
a
1
)
,
where
(
a
1
,
a
2
,
…
,
a
n
)
(a_1, a_2, \dots, a_n)
(
a
1
,
a
2
,
…
,
a
n
)
runs over the set of permutations of
(
1
,
2
,
…
,
n
)
(1, 2, \dots, n)
(
1
,
2
,
…
,
n
)
.
combinatorics
Inequality
maximum value
minimum value
permutations