Two Eggs, 100 Floors

You have two identical eggs and a 100-story building. There exists some floor $k$ such that:

• An egg dropped from floor $k$ or below survives.
• An egg dropped from any floor above $k$ breaks.

You want to find $k$. Eggs that survive a drop can be reused; broken eggs are gone forever. What's the minimum number of drops you need in the worst case to guarantee finding $k$?