Puzzles index

Dividing a circle into different bits

Draw a circle. Now mark a small number of points round the edge of the circle (it's called the circumference). Draw a line between each of the pairs of points. This divides the circle into a number of parts, counting everything bounded by one of these lines, or the edge of the circle. Count them. Now do it for several circles, with the number of points from one (which is a little silly!) up to six. Count the number of parts the circle is divided into each time. Can you spot a pattern?

The points don't have to be evenly spaced around the circle, in fact, it's better if they aren't. The lines cross each other, of course, but you're not allowed to have three lines crossing at a point. If this happens, move one of the points so you get a small part within the three lines. On the other hand, if the points are bunched up too close to each other, the parts can be so tiny that you can't count them. To make it easier for you, this page will count them for you. Click on the buttons and see if you can spot the pattern!

1 point

2 points

3 points

4 points

5 points

6 points