Make a set of numbers that use all the digits from 1 to 9, once and once only.

For instance, we could choose:

638 92 571 and 4

Add them up:

638 + 92 + 571 + 4 = 1305

1305 is divisible by 9 (it is 145 x 9)

(use a calculator to check this if you do not know yet how to divide by 9)

Add each of the digits in the number 1305. What is their sum?

Or, perhaps we could choose:

921 4357 and 68

Add them up:

921 + 4357 + 68 = 5346

5346 is divisible by 9 (it is 594 x 9)

Now try some other possibilities for yourself!

I wonder what happens if we use all 10 digits from 0 to 9, once and once only?

Try some for yourself!

What do you think would happen if we used the eight digits from 1 to 8?

Test you hypothesis by trying some possibilities for yourself!

Were you correct?

Is there a pattern beginning to emerge? Do you have theory that might explain what is happening?

Try some different sets of digits for yourself!