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Let u_1, u_2, \ldots, u_m be m vectors in the plane, each of length \leq 1, with zero sum. Show that one can arrange 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, \ldots, v_m has length less than or equal to \sqrt {5}.

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