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1988 All Soviet Union Mathematical Olympiad
484
ASU 484 All Soviet Union MO 1988 sinx_1+2sin x_2+ ...+nsinx_n=100
ASU 484 All Soviet Union MO 1988 sinx_1+2sin x_2+ ...+nsinx_n=100
Source:
August 8, 2019
trigonometry
system of equations
minimum
algebra
Sum
Problem Statement
What is the smallest
n
n
n
for which there is a solution to
{
sin
x
1
+
sin
x
2
+
.
.
.
+
sin
x
n
=
0
sin
x
1
+
2
sin
x
2
+
.
.
.
+
n
sin
x
n
=
100
\begin{cases} \sin x_1 + \sin x_2 + ... + \sin x_n = 0 \\ \sin x_1 + 2 \sin x_2 + ... + n \sin x_n = 100 \end{cases}
{
sin
x
1
+
sin
x
2
+
...
+
sin
x
n
=
0
sin
x
1
+
2
sin
x
2
+
...
+
n
sin
x
n
=
100
?
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