numbers 1-14 to face and vertices of cube A
Source: Chile Finals 2009 L2 p5
October 5, 2022
combinatorics
Problem Statement
Let and be two cubes. Numbers , are assigned in any order, to the faces and vertices of cube . Then each edge of cube is assigned the average of the numbers assigned to the two faces that contain it. Finally assigned to each face of the cube the sum of the numbers associated with the vertices, the face and the edges on the corresponding face of cube . If is the sum of the numbers assigned to the faces of , find the largest and smallest value that can take.