SEAMO 2027 - Paper F - SET 03 - Self-study Question 14

A real number is assigned to each vertex of cube $ABCDEFGH$, labelled as in the diagram. At each vertex, the average of the numbers at its three adjacent vertices is computed. The averages at $A,B,C,D,E,F,G,H$ are respectively $1,2,3,4,5,6,7,8$. What number was assigned to $F$?

Original source figure, with all mathematical labels retained.