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+-1, at each of the 8 vertices of a given cube, product, sum

Source: Norwegian Mathematical Olympiad 1993 - Abel Competition p4

February 11, 2020

cubecombinatoricscombinatorial geometrySumProduct

Problem Statement

Each of the

8

vertices of a given cube is given a value

1

-1

. Each of the

6

faces is given the value of product of its four vertices. Let

A

be the sum of all the

14

values. Which are the possible values of

A