7. UIUC has just finished constructing the new Reingold Building, the tallest dormitory on campus. In order to determine how much insurance to buy, the university administration needs to determine the highest safe floor in the building. A floor is consdered safe if a drunk student an egg can fall from a window on that floor and land without breaking; if the egg breaks, the floor is considered unsafe. Any floor that is higher than an unsafe floor is also considered unsafe. The only way to determine whether a floor is safe is to drop an egg from a window on that floor. You would like to find the lowest unsafe floor L by performing as few tests as possible; unfortunately, you have only a very limited supply of eggs. (a) Prove that if you have only one egg, you can find the lowest unsafe floor with L tests. [Hint: Yes, this is trivial.]