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IMO Shortlist
1982 IMO Shortlist
11
11
Part of
1982 IMO Shortlist
Problems
(1)
Find the rearrangement
Source: IMO LongList 1982 - P17
9/10/2010
(a) Find the rearrangement
{
a
1
,
…
,
a
n
}
\{a_1, \dots , a_n\}
{
a
1
,
…
,
a
n
}
of
{
1
,
2
,
…
,
n
}
\{1, 2, \dots, n\}
{
1
,
2
,
…
,
n
}
that maximizes
a
1
a
2
+
a
2
a
3
+
⋯
+
a
n
a
1
=
Q
.
a_1a_2 + a_2a_3 + \cdots + a_na_1 = Q.
a
1
a
2
+
a
2
a
3
+
⋯
+
a
n
a
1
=
Q
.
(b) Find the rearrangement that minimizes
Q
.
Q.
Q
.
algebra
Sequence
maximization
minimization
Rearrangement
IMO Shortlist
IMO Longlist