MathDB

On a board the following six vectors are written:

(1, 0, 0), (-1, 0, 0), (0, 1, 0), (0, -1, 0), (0, 0, 1), (0, 0, -1).

Given two vectors

v

and

w

on the board, a move consists of erasing

v

and

w

and replacing them with

\frac{1}{\sqrt2} (v + w)

and

\frac{1}{\sqrt2} (v - w)

. After some number of moves, the sum of the six vectors on the board is

u

. Find, with proof, the maximum possible length of

u

Problem Statement