STARS

When a circle has 8 dots you can move around the circle in steps of length 1, 2, 3, 4, 5, 6 or 7.

If you move around the circle in steps of 2, you miss some points

If you move around the circle in steps of 3, you hit all points.
How else can you hit all points?

When a circle has 9 dots you can hit all points in 6 different ways.
What step sizes allow you to do this?

Now consider 10 points. Can you find the 4 different ways in which we can hit them all?

Explore what happens with different numbers of points and different step sizes and comment on your findings. How can you work out what step sizes will hit all the points for any given number of points?

Now consider 5 points. You can hit all points irrespective of the step size. What other numbers have this property?