cannot each vertex of a cube$ 8$ distinct numbers from 1-12
Source: 2010 Romania District VIII p1
September 1, 2024
combinatoricsnumber theory
Problem Statement
a) Prove that one cannot assign to each vertex of a cube distinct numbers from the set such that, for every edge, the sum of the two numbers assigned to its vertices is even.b) Prove that one can assign to each vertex of a cube distinct numbers from the set such that, for every edge, the sum of the two numbers assigned to its vertices is divisible by .