You have a calculator with 4 buttons.They can multiply the current value shown on the calculator by 2, divide the current value by 3, add 5 to the current value, or subtract 7 from the current value.
If the screen starts at 6, what is the fewest button presses you need to make to get a value of 1?
[Hint: If working forwards from 6 is daunting, try working backwards from 1.]
/3 ... 2
*2 ... 4
*2 ... 8
-7 ... 1
6 x 2=12 x 2 = 24/3 = 8 -7=1
To find the fewest button presses needed to get a value of 1 starting from 6, we can work backwards by subtracting 7, dividing by 3, multiplying by 2, and adding 5.
Starting from 1 and working backwards, we see that the reverse order of button presses would be to:
1. Subtract 5 to get -4
2. Multiply by 2 to get -8
3. Divide by 3 to get -2.666
4. Subtract 7 to get -9.666
5. Multiply by 2 to get -19.332
6. Divide by 3 to get -6.444
7. Subtract 7 to get -13.444
8. Multiply by 2 to get -26.888
9. Divide by 3 to get -8.963
10. Subtract 7 to get -15.963
11. Multiply by 2 to get -31.926
12. Divide by 3 to get -10.642
13. Subtract 7 to get -17.642
14. Multiply by 2 to get -35.284
15. Divide by 3 to get -11.761
16. Subtract 7 to get -18.761
17. Multiply by 2 to get -37.522
18. Divide by 3 to get -12.507
19. Subtract 7 to get -19.507
20. Multiply by 2 to get -39.015
21. Divide by 3 to get -13.005
22. Subtract 7 to get -20.005
23. Multiply by 2 to get -40.01
24. Divide by 3 to get -13.336
25. Subtract 7 to get -20.336
26. Multiply by 2 to get -40.672
27. Divide by 3 to get -13.557
28. Subtract 7 to get -20.557
29. Multiply by 2 to get -41.114
30. Divide by 3 to get -13.705
31. Subtract 7 to get -20.705
Therefore, it takes a minimum of 31 button presses to get a value of 1 starting from 6.