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?

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.

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.

Arrange the Digits

Age 11 to 14 Challenge Level

Can you arrange the digits $1,2,3,4,5,6,7,8,9$ into three $3$ -
digit numbers such that their total is close to $1500$?

You might like to think about how many different ways there are of
getting as close as you can to $1500$.