### 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.

### Sending Cards

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

# The 24 Game

##### Stage: 2 Challenge Level:

Here are some solutions from Jessica from Woodbridge High School, Essex. James from Hethersett High School sent his solutions which appear on one or other of the lists below. Can you find yet more?

 1. (4 - 6/6) x 8 2. 8 x (4 - 6/6) 3. (6 + 6) x 8/4 4. 8/4 x (6 + 6) 5. (6 + 6)/4 x 8 6. 6 x 8 - 6 x 4 7. 6 x 8 - 4 x 6 8. 8 x 6 - 6 x 4 9. 8 x 6 - 4 x 6 10. 4+6+6+8 11. 4+8+6+6 12. 4+6+8+6 13. 6+6+4+8 14. 6+6+8+4 15. 8+4+6+6 16. 8+6+4+6 17. 6+8+4+6 18. 6+4+8+6 19. 8+6+6+4 20. 6 x 6 - (8 + 4) 21. 6 x 6 - 4 - 8 22. 6 x 6 - 8 - 4 23. 6 x 6 - (4 + 8) 24. (6 - 8/4) x 6 25. 6 x (6 - 8/4) 26. 8[6/(6 - 4)] 27. [6/(6 - 4)] x 8

Pupil from the Mount School, York sent the following:

We couldn't find 60 just by using the four arithmetic rules and found ourselves using other functions like those shown in the examples below: $$(8 - 4)! \times 6 \div 6$$ or $$(8 - 4)! + 6 - 6$$ The other thing we discovered was that many of our solutions that we thought were different, were in fact exactly the same, like $$\frac{8}{4} \times (6 + 6)$$ and $$(6 + 6) \times 8/4$$ Here are some solutions:

\begin{eqnarray} 4 + 6 + 6 + 8 &=& 24 \\ (6 + 6) + (8 + 4) &=& 24 \\ (6 \times 8) - (4 \times 6) &=& 24 \\ 8 \times ( 6 \div ( 6 - 4)) &=& 24 \\ (6 \times 8) \div (6 - 4) &=& 24 \\ (4 - (6 \div 6)) \times 8 &=& 24 \end{eqnarray}