12-Ball Challenge!

I love these puzzles that have shown up recently in the blogsphere. Ben Wright has had several “Guess the author” games over at Paleoevangelical and Larry Rogier has a logic riddle online now at his blog, Stuff Out Loud. These games are great fun, especially when you can figure out the answer. :)

My favorite puzzle is the one that my father-in-law posed one Thanksgiving dinner prior to my engagement and marriage to his daughter. Somehow we got on the subject of riddles and puzzles, everyone throwing out their own little puzzle when finally my future father-in-law challenged us with his puzzle and claimed that no one would be able to solve it without a hint from him! At the time, I was working as a cryptomathematician for the National Security Agency and I took it as somewhat of a professional challenge. I certainly wasn't going to ask for a hint without giving it a decent try on my own. Daphne and I worked on it together over Christmas as we flew out to California for her to meet my parents but we really didn’t get very far. It was indeed a tough puzzle. I don’t remember how or when but I finally figured out the trick that unlocked the solution. After our trip, I presented the puzzle to several of my colleagues at work, some of them PhD mathematicians. One said it was impossible to solve because it violated Shannon’s law of information theory. This particular individual was not happy when I showed him the solution.

At any rate, then next time I visited Daphne at her home, I sat down with her father and told him I had a solution to his puzzle. With a bit of skepticism, he listened to me as I not only solved the 12-ball problem but showed how it could be extended and solved up to 15 balls. He was both impressed and pleased, I think, that someone was able to solve his riddle. I wasn’t finished, though. I told him that I wanted a reward for solving his impossible puzzle – his daughter’s hand in marriage! Alright, I’m a geek. I admit it. But that is the story of how I secured my father-in-law’s permission to marry his daughter. By the way, his 6-year old grandson, JD, is pretty good at solving puzzles himself now, too.

Oh, here is the puzzle:

You have 12 balls. They are all the same in color and size. They all weigh the same except for one ball. The challenge – find the odd-weighted ball in 3 or less weighings using a balance scale.

You can probably find this on the Internet so no fair using Google!