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 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.
Pairing Up
Age 11 to 14 Short Challenge Level
The numbers $72, 8, 24, 10, 5, 45, 36, 15$ are grouped in pairs so that each pair has the same product. Which number is paired with $10$?
If you liked this question, here is an NRICH task which challenges you to use similar mathematical ideas.