One of my colleagues was asked the following brain teaser or puzzle during an interview at Goldman Sachs & Co.:

You have two identical breakable objects, such as glass pebbles. You are standing in front of a 100-story building and you are told that staring at certain floor, the objects start breaking as you drop them off the balcony. What is the optimal (i.e. minimum number of tries) solution to find out which floor the objects start breaking at?

For example, you can take the approach of binary search. Drop the object down from the 50th floor. If it breaks, you will have to start from the second floor and if the floor you are looking for is truly the 50th, you will have to try 48 more times, totaling in 49 tries. If the object didn’t break, you can try the 75th floor, etc. This, however, is not the optimal solution.

I asked my friend, Radu Gabudean, to solve the question. He told me that I had asked him the same question a year ago and that he had already told me the solution. I challenged him by saying that I wasn’t sure what he was talking about and if he wanted me to take him seriously at all, he should prove it. Two hours later, he sent me the solution and the proof. Don’t mess with the finance PhDs!