Why 61?
Here is a small piece of quote from Scientific American May 95 issue, Mathematical Recreation. The quote is really very interesting, but the article is far more interesting than just this quote. Believe me -- go read the real thing.
"Any good at math at school," I finished. "That's what they all say."
"Hated it then," Athanasius mumbled. "Still do."
"I must be the exception!" a voice boomed at my right. "Absolutely love it! Name's Adam Smasher. I'm a nuclear physicist. I have a little puzzle I'll ask all of you. What's the next number in the sequence 1, 1, 2, 3, 5, 8, 13, 21?"
"Nineteen," I grunted automatically, while battling with a bread roll seemingly baked with cement.
"You're not supposed to answer," he said. "Anyway, you're wrong -- it's 34. What made you think it was 19?"
I drained my glass. "According to Carl E. Linderholm's great classic Mathematics Made Difficult, the next term is always 19, whatever the sequence: 1, 2, 3, 4, 5 - 19 and 1, 2, 4, 8, 16, 32 - 19. Even 2, 3, 5, 7, 11, 13, 17 - 19."
"That's ridiculous."
"No, it's simple and general and universally applicable and thus superior to any other solution. The Laplace interpolation formula can fit a polynomial to any sequence whatsoever, so you can choose whichever number you want to come next, having a perfectly valid reason. For simplicity, you always choose the same number."
"Why 19?" Dennis asked.
"It's supposed to be one more than your favorite number," I said, "to fool anyone present who likes to psychoanalyze people based on their favorite number."
Copyright notice: the material is copyrighted by Scientific American.