Challenge 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

Excellent Martha - thank you for sharing your answer with us.