You are doing a stress test on a particular model of smart phones. You

have a ladder with n rungs. You want to determine the highest rung

from which you can drop a phone without it breaking and you want

to do it with the smallest number of phone drops.

$$ Imagine that you have exactly $2$ phones. Devise an algorithm

that can determine the highest safe rung using o$($n$)$ drops.

$$ Now suppose you have k phones. Devise an algorithm that can

determine the highest safe rung with the smallest number of

drops. If fk$($n$)$ is the number of drops that your algorithm

needs, what is fk$($n$)$ asymptotically? Hint: you should ensure

that fk$+1($n$)=$ o$($fk$($n$))$ for any k