### Repeaters

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

### Big Powers

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

# Back to the Planet of Vuvv

### Why do this problem?

This problem one which requires some knowledge of both place value and different bases. Working in another base can help with real understanding of our base-$10$ number system.

You could start this by either explaining or re-visiting counting in a base such as $6$. Base $7$ could be introduced using the days of a week as an example.

### Key questions

If Zios count in $3$s, what will their first 2-digit number be in human numbers?
If Zepts count in $7$s, what will their first 2-digit number be in human numbers?
What is $122, 22, 101, 41$ in Zio counting?
What is $122, 22, 101, 41$ in Zept counting?
Would drawing a sketch help with sorting out the four compass points?

### Possible extension

Learners could make a similar puzzle for themselves, or go on to this similar problem: Basically.

### Possible support

Suggest trying Alien Counting instead which is a simpler problem of the same type.