Question 4
There are 8 identical dice. The numbers $4$, $5$, $6$ are written on three faces of the dice, as shown in the figure, and the remaining faces carry the numbers $1$, $2$, $3$ so that the sum of the numbers written on each pair of opposite faces is $7$.
a) Show that using these dice, it is possible to form a $2 \times 2 \times 2$ cube so that every two faces that touch each other carry the same number.
b) Is it possible to do this in such a way that only numbers $4$, $5$, $6$ occur on the outer surface of the resulting cube?
a) Show that using these dice, it is possible to form a $2 \times 2 \times 2$ cube so that every two faces that touch each other carry the same number.
b) Is it possible to do this in such a way that only numbers $4$, $5$, $6$ occur on the outer surface of the resulting cube?