How to count without...well, counting.

Imagine you are throwing a party.  You have hired the local community hall and round the walls are stacked a load of fold-up chairs.  As more and more people arrive you start to worry about whether there are enough chairs for everybody. What to do? Well, you could try counting the number of people there - difficult if they're all moving round, which they probably are - and then counting the number of chairs, but an easier solution is to get everybody's attention and then ask everybody to get a chair and sit on it.  If you are left with people still standing you know you've got more people than chairs, if everybody is seated and there are still chairs unused you know you've got more chairs than people, and if everybody is sitting down and there are no chairs left you know you've got the same number of chairs and people,  But the point is that you haven't counted - you still don't know how many people are there or how many chairs. Have a feeling this could be the start of a series of posts.