MathDB
ASU 193 All Soviet Union MO 1974 n vectors in space, sum less than 2

Source:

July 4, 2019
vectorcombinatorial geometrycombinatorics

Problem Statement

Given nn vectors of unit length in the plane. The length of their total sum is less than one. Prove that you can rearrange them to provide the property:
for every k,knk, k\le n, the length of the sum of the first kk vectors is less than 22.