Question 45
What is the smallest $n$ for which there is a solution to
$$\sin x_{1} + \sin x_{2} + \ldots + \sin x_{n} = 0,$$
$$\sin x_{1} + 2 \sin x_{2} + \ldots + n \sin x_{n} = 100?$$
$$\sin x_{1} + \sin x_{2} + \ldots + \sin x_{n} = 0,$$
$$\sin x_{1} + 2 \sin x_{2} + \ldots + n \sin x_{n} = 100?$$