Question 17
The vertices of a cube are enumerated by the numbers $1$, $2$, $\ldots$, $8$. Someone chose three sides of the cube and told the numbers which are written on them to Pete: $\{1, 4, 6, 8\}$, $\{1, 2, 6, 7\}$, $\{1, 2, 5, 8\}$. Is it possible to determine which number has the vertex which is opposite to the one numbered $5$?