Make a set of numbers that use all the digits from 1 to 9, once and
once only. Add them up. The result is divisible by 9. Add each of
the digits in the new number. What is their sum? Now try some other
possibilities for yourself!
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.
Missing Digit
Age 11 to 14 Short Challenge Level
The 8-digit number 1234_678 is a multiple of 11.
What is the missing digit?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.