Numbers in a cube
Source: Problem 1 - Brazil Math Olympiad 1994
March 17, 2006
geometry3D geometrycombinatorics proposedcombinatorics
Problem Statement
The edges of a cube are labeled from 1 to 12 in an arbitrary manner. Show that it is not possible to get the sum of the edges at each vertex the same.
Show that we can get eight vertices with the same sum if one of the labels is changed to 13.