Challenge Level

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

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

Here is one of the ways in which you can do it:

Here is another way you can do it:

**In how many different ways can it be done?**

**Now try with a stick of eight cubes:**

**What about with a stick of six cubes?**

**What do you notice?**

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

Try it! Were you right?

How many ways with 20 cubes?

**Will your noticing always be true? Can you create an argument that would convince mathematicians?**