In Google Code Jam this year, there was a problem called "Cheating Detection" that was very different from the usual algorithm-based problems. It was more data-driven: it involved finding the cheater among a set of students, given only the scores of all students in each of the questions in an exam, and the mechanism of cheating that the cheater used (cheating only 50% of the time).

After the round was over, I went to see the solutions of the top contestants, to see what sorts of methods they used to obtain a solution. The solution had to detect the cheater with very high probability, and also needed to be a fast enough program to type that it would be among the first submitted. I found the top solution to be surprisingly simple in its code, so I tried to figure out a mathematical explanation for why it worked. I ended up making a video with this explanation.

You can watch the video here: