numbering edges of cube from 1 to 12
Source: 1986 German Federal - Bundeswettbewerb Mathematik - BWM - Round 2 p1
November 21, 2022
combinatorics
Problem Statement
The edges of a cube are numbered from to , then is calculated for each vertex the sum of the numbers of the edges going out from it.
a) Prove that these sums cannot all be the same.
b) Can eight equal sums result after one of the edge numbers is replaced by the number ?