### Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

### I'm Eight

Find a great variety of ways of asking questions which make 8.

### Dice and Spinner Numbers

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

# Book Codes

##### Stage: 2 Challenge Level:

From any ISBN code we can calculate a 'check total' by multiplying the digits in the code by $1, 2, 3, \ldots$ in order and adding these products. For example $0 - 04 - 823208 - 4$ gives $$(1\times0) + (2\times0) + (3\times4) + (4\times8) + (5\times2) + (6\times3) + (7\times2) +$$ $$+(8\times0) + (9\times8) + ( 10\times4) = 198$$

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 was sent in by  Abbas from Jack Hunt School, Peterborough, for a previous version of the problem, in which we asked you to calculate the missing digit in this ISBN: $$0 - 947?95 - 24 - 3$$.

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

In the ISBN 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

Well done Abbas!

Please send us your solutions to the updated problem - you can find it here