MathDB

Let

v_1, v_2, \ldots, v_{1989}

be a set of coplanar vectors with

|v_r| \leq 1

for

1 \leq r \leq 1989.

Show that it is possible to find

\epsilon_r

1 \leq r \leq 1989,

each equal to

\pm 1,

such that \left | \sum^{1989}_{r\equal{}1} \epsilon_r v_r \right | \leq \sqrt{3}.

57