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Putnam
2018 Putnam
A3
Putnam 2018 A3
Putnam 2018 A3
Source:
December 2, 2018
Putnam
Putnam 2018
Problem Statement
Determine the greatest possible value of
∑
i
=
1
10
cos
(
3
x
i
)
\sum_{i = 1}^{10} \cos(3x_i)
∑
i
=
1
10
cos
(
3
x
i
)
for real numbers
x
1
,
x
2
,
…
,
x
10
x_1, x_2, \dots, x_{10}
x
1
,
x
2
,
…
,
x
10
satisfying
∑
i
=
1
10
cos
(
x
i
)
=
0
\sum_{i = 1}^{10} \cos(x_i) = 0
∑
i
=
1
10
cos
(
x
i
)
=
0
.
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