Question 22
Every face of a unit cube has one of numbers $-1$, $0$, $1$ written on it in such a way that every two faces with a common edge contain different numbers. Is it possible to form
a) a cube of size $2 \times 2 \times 2$;
b) a cube of size $3 \times 3 \times 3$
so that in the grids that come up on the faces, every two squares with a common side contain different numbers and the sum of all numbers on each face equals $0$?
a) a cube of size $2 \times 2 \times 2$;
b) a cube of size $3 \times 3 \times 3$
so that in the grids that come up on the faces, every two squares with a common side contain different numbers and the sum of all numbers on each face equals $0$?