Minimal Sum of Squares
Source: 2013 Baltic Way, Problem 5
December 30, 2013
geometry3D geometryalgebra unsolvedalgebra
Problem Statement
Numbers and are written at two opposite vertices of a cube. Some real numbers are to be written at the remaining vertices of the cube. On each edge of the cube the difference between the numbers at its endpoints is written. When is the sum of squares of the numbers written on the edges minimal?