Question 9
In the diagram below, ten beads labelled as $A,B,C,D,E,F,G,H,I,J$ are arranged in clockwise order on a circle, where bead $A$ is labelled $9$ and bead $F$ is labelled $10$. The remaining eight beads are to be labelled with the numbers $1,2,3,4,5,6,7,8$, using each number exactly once. If the number on $G$ must be greater than the number on $E$ and the sum of the numbers of any two adjacent beads must be a prime number, list down all different possible labellings.
(Note: The number of correct answers minus the number of incorrect answers is the net correct answer, $2$ marks for each net correct answer. Finding all correct answers without any incorrect answer gives $40$ marks.)
(Note: The number of correct answers minus the number of incorrect answers is the net correct answer, $2$ marks for each net correct answer. Finding all correct answers without any incorrect answer gives $40$ marks.)