BG-MO 2003 Problem 1

Let $x_1, x_2 \ldots , x_5$ be real numbers. Find the least positive integer $n$ with the following property: if some $n$ distinct sums of the form $x_p+x_q+x_r$ (with $1\le p<q<r\le 5$ ) are equal to $0$ , then $x_1=x_2=\cdots=x_5=0$ .