The interview was booked through a talent hunter.

This was the second time I had interviewed with Goldman Sachs, but having no great interest in working for this firm, I had not prepared at all.

The first part of the interview consisted of an introduction to the work in the department, which was not sufficiently detailed.

Then, I was asked to present the work I had performed during past jobs and during my PhD.

Subsequently, I was asked to state the fields in which I considered myself strongest.

The second part of the interview consisted of two questions: one in probability and the other in number theory.

The first question was easy, and the second should be easy for those accustomed to number theory.

In a corridor with 100 lockers, you pass the first time and open each locker.

Then, you pass the second time and close each second locker.

Subsequently, you pass the third time and toggle the state of each third locker, then you pass again each fourth, and so on...

You repeat this process 100 times.

How many lockers are open at the end?