Why do this problem?
can be seen as one to introduce multibase work. Many articles have been written about the use of working in different bases. Some of you will remember using Dienes Multibase Blocks for the same purpose. It can certainly be of use to help pupils really get a better grip of the four rules of number
and what is happening when we are working in our own base ten.
On the other hand it is a useful investigation in its own right and from the multiplication table many patterns can be found. It is good to encourage pupils to get to the reasons WHY these patterns and relationships occur.
It is possible to have aliens that have nine "fingers" instead of ten. You can then go through some simple counting and adding on as if you are this nine-fingered alien.
Having done this outloud, you could introduce the way of writing the numbers to the group before suggesting they continue themselves.
Tell me about this counting in groups of $9$.
You might find it very useful to explore the similarity with multiplying by $8$ in this system compared to using $9$ in the base $10$ system.
There are strong links to digital roots which you can read about here.
There are also some other NRICH challenges that could be worthwhile looking at after this one: Consecutive Numbers
(Exploring Wild & Wonderful Number Patterns).
Some children will find it useful to have something that can show the number nine physically - a toy alien with nine fingers for example.