2005 AMC 8 Problems/Problem 24
Problem
A certain calculator has only two keys [+1] and [x2]. When you press one of the keys, the calculator automatically displays the result. For instance, if the calculator originally displayed "9" and you pressed [+1], it would display "10." If you then pressed [x2], it would display "20." Starting with the display "1," what is the fewest number of keystrokes you would need to reach "200"?
Solution
hI kIDS i am bob AND I SHALL EAT YOU. NEVETR COME AND TRY TO HURT ME. I AM THE GOD OF HACKING YOur butt smells
First we can start at 200 and work our way down we want to do /2 the most so if we come across an odd number we just subtract 1! So 
=100, 100/2=50, 50/2=25, 25-1=24, 24/2=12, 12/2=6, 6/2=3, 3-1=2, and 2/2=1. We made our way back to 1 but since it is the amount of times the button is pressed than the answer should be \boxed{\textbf{(B)}\ 9}$.
See Also
| 2005 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 23 |
Followed by Problem 25 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
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