Question 24
A certain calculator has only two keys [$+1$] and [$\times 2$]. 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 [$\times 2$], it would display “$20.$” Starting with the display “$1,$” what is the fewest number of keystrokes you would need to reach “$200$”?