Well, perhaps I cheated "a little" in the following sense. I was having a very hard time trying ever more complicated algorithms (for a few days

), obviously getting nowhere, even though the fact that it is simple is given away in the story.
Then I saw the response times (and just those!) of the people that solved it and ... just sat back, looked at the problem in a completely differrent way and it immediately came to me
And now I must keep the vows of the fraternity and not divulge the secret to ... my fiancee