The 24 Game

'The 24 Game' printed from https://nrich.maths.org/

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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}