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 1 (Now rigorous)
We can start at and work our way down to . We want to press the button that multiplies by the most, but since we are going down instead of up, we divide by instead. If we come across an odd number, then we will subtract that number by . Notice
, , , , , , , , .
Since we've reached , it's clear that the answer should be - . Because we only subtracted when we had to, this is optimal. ~Roy2020
can someone please rigor this
See Also
2005 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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