4

Part of 1993 Abels Math Contest (Norwegian MO)

Problems(1)

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

Source: Norwegian Mathematical Olympiad 1993 - Abel Competition p4

8

vertices of a given cube is given a value

1

-1

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

cubecombinatoricscombinatorial geometrySumProduct