### 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

##### Age 11 to 14Challenge Level

Martha in Year 5 at Hatherleigh Primary School has sent us a very well explained solution to this tricky problem. She says:

First I counted up to $122$ in base $3$ and base $7$. Then I marked them off in fives in base $10$.

Here is her working:

She goes on to say:

After that I wrote down the four numbers we were given, found out what they were in base $3$ and $7$, and worked out whether or not they could be made out of $7$s and $3$s:

$22$ and $41$ could only be in base $7$ so the other two were Zios. So:

West - Zio
East - Zept
South - Zio
North - Zept