Consider the following problem, a popular Google interview question:

A firm has invented a super-strong egg. For publicity purposes, it wants to determine the highest floor in a story building of n floors from which such an egg can fall without breaking. The firm has given a tester two identical eggs to experiment with. The same egg can be dropped multiple times unless it breaks.

For a n floor story building, what is the minimum number of droppings d that is guaranteed to determine the highest safe floor in all cases?