You may also like

Double Digit

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. Try lots of examples. What happens? Can you explain it?

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 14
Challenge Level

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.