I remember that few years ago I was given this exact stock problem on some interview at some company. What followed then was an hour of me stating bunch of false lemmas and being literally clueless about it. I was kinda destroyed that I was rejected not because of I am bad at writing clean code, not because I am bad at some system design or class diagrams, but because I failed at solving algorithmic question which is my beloved hobby, what was a real stain on my honor and dignity. I feel kinda relieved to read that one of the greatest competitive programmers in world wrote "Problem D had deceptively simple statement which led to a lot of frustration as I was unable to come up with its solution for two hours" :P (however I wouldn't call getting it accepted at 2:00 mark as a fifth problem as being unable to solve it for two hours, but you get the point).