Question 8
(FRA 3) Let $u_1,u_2,\ldots,u_m$ be $m$ vectors in the plane, each of length less than or equal to $1$, which add up to zero. Show that one can rearrange $u_1,u_2,\ldots,u_m$ as a sequence $v_1,v_2,\ldots,v_m$ such that each partial sum $v_1,v_1+v_2,v_1+v_2+v_3,\ldots,v_1+v_2+\cdots+v_m$ has length less than or equal to $\sqrt5$.