You are conducting a highly sophisticated physics experiment in a building with 100 floors. What you wish to know is how high you can drop an egg without it breaking. We assume there is no wind and no external forces and no randomness to it, there exists an N, 0<=N<=100, such that the egg breaks at floor N, but not in N-1.
However, the physics department's funding has been recently cut, and you only have two eggs. You are also in a hurry, so you wish to conduct your experiment as fast as possible. Being a pessimistic person, you want your experiment to be as fast as possible not in average, but in worst-case scenario. That is, you want to bound the maximum number of trials that may result in your method. How would you go about that?