The 24 game
Problem
Using all four numbers 4, 6, 6 and 8, but using each number only once, there are over 60 different ways of getting the answer 24 by adding, subtracting, multiplying and dividing.
How many can you and your friends find?
Student Solutions
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: