MathDB

5

Part of 2009 Chile National Olympiad

Problems(1)

numbers 1-14 to face and vertices of cube A

Source: Chile Finals 2009 L2 p5

10/5/2022
Let AA and BB be two cubes. Numbers 1,2,...,141,2,...,14, are assigned in any order, to the faces and vertices of cube AA. Then each edge of cube AA is assigned the average of the numbers assigned to the two faces that contain it. Finally assigned to each face of the cube BB the sum of the numbers associated with the vertices, the face and the edges on the corresponding face of cube AA. If SS is the sum of the numbers assigned to the faces of BB, find the largest and smallest value that SS can take.
combinatorics