MathDB
Less than SQRT(3)

Source: IMO Longlist 1989, Problem 57

September 18, 2008
vectorcombinatorics unsolvedcombinatorics

Problem Statement

Let v1,v2,…,v1989 v_1, v_2, \ldots, v_{1989} be a set of coplanar vectors with ∣vr∣≤1 |v_r| \leq 1 for 1≤r≤1989. 1 \leq r \leq 1989. Show that it is possible to find ϵr \epsilon_r, 1≤r≤1989,1 \leq r \leq 1989, each equal to ±1, \pm 1, such that \left | \sum^{1989}_{r\equal{}1} \epsilon_r v_r \right | \leq \sqrt{3}.
Back to ProblemsView on AoPS