16. Five girls ran a race. Fiona started first, followed by Gertrude, then Hannah, then India and lastly Janice. Whenever a girl overtook another girl, she was awarded a point. India was first to finish, then Gertrude, then Fiona, then Janice and lastly Hannah. What is the lowest total number of points that could have been awarded?
A 9
B 8
C 7
D 6
E 5
SolUTION
E

Representing the girls by their first initial, and using the left as the front of the race, the initial position is FGHIJ. For I to win, she must at some point overtake F, G and H, earning three points. For $\mathrm{G}$ to be second, she must overtake F, earning one point. For $\mathrm{J}$ to be fourth, she must overtake $\mathrm{H}$, earning one point. Hence a minimum of five points must be awarded. One possible set of positions during the race could be FGHIJ, FGIHJ, FIGHJ, IFGHJ, IGFHJ, IGFJH, with each change earning one point.