Question

Some girls are standing in a circle. The teacher makes them do a headcount. Bianca says one, her neighbour says two and so on. If they count in a clockwise direction, Antonia says five. If they count in an anticlockwise direction, Antonia says eight. How many girls are forming the circle?

Answer 1

11

Explanation:

See the attached image: the outer numbers count girls clockwise, showing Antonia at point J. The inner numbers show counting anticlockwise, showing Antonia as number 8, then continuing the count past her.

Aha! The inner and outer numbers always sum to 13.

But anticlockwise #12 really counted herself as #1 (she's being counted twice), so there aren't 12 girls, there are 11.

If you're not convinced, draw a picture with, say, 5 girls in it, number them counting both ways.