AMC8
2005
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"?