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11
2000 Guts #11: Maximum value
2000 Guts #11: Maximum value
Source:
October 12, 2014
Problem Statement
Let
M
M
M
be the maximum possible value of
x
1
x
2
+
x
2
x
3
+
⋯
+
x
5
x
1
x_1x_2+x_2x_3+\cdots +x_5x_1
x
1
x
2
+
x
2
x
3
+
⋯
+
x
5
x
1
where
x
1
,
x
2
,
⋯
x
5
x_1, x_2, \cdots x_5
x
1
,
x
2
,
⋯
x
5
is a permutation of
(
1
,
2
,
3
,
4
,
5
)
(1,2,3,4,5)
(
1
,
2
,
3
,
4
,
5
)
and let
N
N
N
be the number of permutations for which this maximum is attained. Evaluate
M
+
N
M+N
M
+
N
.
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