This investigation is probably best suited to children above age seven. Plenty of accurate adding needs to be done! Although the ability to do division is called for, calculators could be used to perform the operation as well as to check results.

For younger learners and children still working on basic operations, the task could be to could be to find different 2-digit numbers the set of digits 1-9, and then total these adding in the 'extra' digit and work from this total. This activity leads children to generate for themselves the rule for divisibility by 9 - that if the digits in a number add to 9 or a multiple of 9 (the digits of which can always be added and reduced to 9) - then the original number is divisible by 9. For example, take 5346:

5 + 3 + 4 + 6 = 18

1 + 8 = 9

The more able pupils could explore what multiples of 9 they can and cannot make using all the digits 1-9 once and once only.These will be between 45 (the result of adding all nine digits as 1-figure numbers) and 987654321 + 1

Similarly, the totals of other digit sets - 1 through 8, 0 through 9 e.t.c., can be explored to reveal the defining properties of divisibility. Some questions to be asked are: Is the total always odd or even, or can it be either? Do the units or ones digits in a set of totals follow a pattern? Is there anything interesting to report when the digits of the totals are added together until you have a single digit answer?