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