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# Break it Up!

##### Age 5 to 11 Challenge Level:

You have a stick of $7$ interlocking cubes. You cannot change the order of the cubes. You break off a bit of it leaving it in two pieces.

Here are $3$ 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:  Make a table of your results like this:

 Number of cubes Number of ways $6$ cubes ? $7$ cubes ? $8$ cubes ?

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

Were you right?

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

ANY number of cubes?

* * * * * * * * * * * * * * * * * * * *

If all the cubes are the same colour, a split of $4$ and $2$ will look the same as a split of $2$ and $4$.

How many ways are there of splitting $6$ cubes now?

Can you predict how may ways there will be with any number of cubes?