Challenge Level

You have a stick of 7 interlocking cubes (or a tower of 7 Lego blocks). You cannot change the order of the cubes.

You break off a bit of it leaving it in two pieces.

Here are three of the ways in which you can do it:

In how many different ways can it be done?

Now try with a stick of 8 cubes and a stick of 6 cubes:

Now predict how many ways there will be with 5 cubes.

Try it! Were you right?

How many ways with 20 cubes? 50 cubes? 100 cubes?

ANY number of cubes?