193

Part of 1974 All Soviet Union Mathematical Olympiad

Problems(1)

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

Source:

n

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, k\le n

, the length of the sum of the first

k

vectors is less than

2

vectorcombinatorial geometrycombinatorics