Interview Maths Puzzle Numerical Ability

There is a building of 100 floors If an egg drops from the Nth floor or above it will break If it’s dropped from any floor below, it will not break You’re given 2 eggs Find N, while minimizing the number of drops for the worst case.

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Interview Other Question

Two MIT math grads bump into each other while shopping. They haven't seen each other in over 20 years. First grad to the second: "How have you been?"
Second: "Great! I got married and I have three daughters now."
First: "Really? How old are they?"
Second: "Well, the product of their ages is 72, and the sum of their ages is the same as the number on that building over there..."
First: "Right, ok... Oh wait... Hmm, I still don't know."
Second: "Oh sorry, the oldest one just started to play the piano."
First: "Wonderful! My oldest is the same age!"
How old was the first grad’s daughter?
I have a box of one hour fuses. If I set one end of a fuse on fire, I know that the fuse will burn all the way to the other end in EXACTLY one hour. However, the fuses may burn unevenly [ie - it may take 59 minutes to burn the first half of a fuse, but only 1 minute to burn the other half]. Furthermore, all of the fuses may burn unevenly at a different rate. The only thing we know for sure is that each one takes 1 HOUR to burn completely. The Question: Given 2 of these fuses and a lighter, how can I time out 45 minutes precisely?