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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.

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Back to the Planet of Vuvv

Age 11 to 14
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:

Martha's 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:

The second part of Martha's working.

$22$ 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.