2005 AMC 8 Problems/Problem 24: Difference between revisions
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==Solution== | ==Solution== | ||
It is easier to work backwards from <math>200</math>, and have keys that display [-1] and [x0.5]. Use the second key when the number is | It is easier to work backwards from <math>200</math>, and have keys that display [-1] and [x0.5]. Use the second key when the number is e | ||
This takes <math>\boxed{\textbf{(B)}\ 9}</math> keystrokes. | This takes <math>\boxed{\textbf{(B)}\ 9}</math> keystrokes. | ||
ven, and the first key when the number is odd until you get one. We get: | |||
YOur butt smells | |||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2005|num-b=23|num-a=25}} | {{AMC8 box|year=2005|num-b=23|num-a=25}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 15:23, 27 September 2020
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
It is easier to work backwards from 
, and have keys that display [-1] and [x0.5]. Use the second key when the number is e
This takes 
keystrokes.
ven, and the first key when the number is odd until you get one. We get:
YOur butt smells
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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: Unable to save thumbnail to destination
