Riddle: Dropping Eggs from a Building
You stand before a 100-story building with two eggs. Using only these two eggs, you must figure out the highest floor from which you can drop an egg such that the egg won't break when it hits the ground (we'll call this the "highest safe floor"). Every floor is equally likely to be the highest safe floor, including the top floor, and it's also just as likely that the egg will break from every floor. You can assume that if you drop an egg and it doesn't break, its shell is just as strong as it was before you dropped it.
If you want to minimize the expected number of drops you have to perform, what strategy should you use for picking which floors to drop the eggs from? You should write a program to solve this problem.
How can solving this problem on a shorter building help you solve it for solving it with taller buildings?