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Adding All Nine

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!

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.

Magic Potting Sheds

Age 11 to 14 Challenge Level:

For another problem that builds on the ideas in this problem, students can be directed to More Magic Potting Sheds

Full details of a tried and tested classroom approach to this problem can be found in the Notes to More Magic Potting Sheds

This activity offers students the opportunity to explore a new environment and challenges them to use some deductive reasoning. The problem can be tackled on paper but access to the interactivity will speed up the process of exploring different possibilities.
It is important to have paper available for students to record the results of the different trials.