This question was one among the 4 I had to face at the Google Code Jam 2014 Qualification round. I only managed to solve two - Magic Trick (this one) & Cookie Clicker Alpha (read). Although I managed to get qualified with 25 points in total, finishing at 13063 :). This one was the easiest to understand. You can read the problem Statement here. If you are interested you can also refer to Cookie clicker Alpha.