From any ISBN code we can calculate a 'check total' by multiplying the digits in the code by

1, 2, 3, \dots

in order and adding these products. For example

0 - 04 - 823208 - 4

gives

(1 x 0) + (2 x 0) + (3 x 4) + (4 x 8) + (5 x 2) + (6 x 3) + (7 x 2) + (8 x 0) + (9 x 8) + (10 x 4) = 198 .

Try this for yourself with any ISBN number and the check total will always be divisible by 11. This calculation is used to check that the book number has been copied down accurately and thus to avoid errors in placing orders.

This solution is from Abbas from Jack Hunt School, Peterborough. Well done Abbas!

What I noticed is that all the answers have one thing in common. They are all divisible by 11.

In the ISDN code

$0 - 947 ? 95 - 24 - 3$

the question mark must be replaced by the number 7. This is the smallest number that gives a check total that is exactly divisible by 11. See the working below.

Multiplier 1 2 3 4 5 6 7 8 9 10 Total:

ISBN Number 0 9 4 7 7 9 5 2 4 3

Product 0 18 12 28 35 54 35 16 36 30 264 = 24 x 11

Multiplier	1	2	3	4	5	6	7	8	9	10	Total:
ISBN Number	0	9	4	7	7	9	5	2	4	3	Total:
Product	0	18	12	28	35	54	35	16	36	30	264 = 24 x 11