This problem has been designed to be worked on in a group. For more details about how you might go about doing this, please read the Teachers' Notes.

Here are nine different cogs:




If you coloured one tooth on each cog, which pairs of cogs let the coloured tooth go into every 'gap' on the other cog?

Which pairs do not let this happen? Why?

Can you explain how to determine which pairs will work, and why?

You could cut out the cogs from these sheets or you could use the cogs interactive environment to try out your ideas.