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The Little Old Man With Good Teeth and Shaky Hands: Puzzling Logic

The Little Old Man With Good Teeth and Shaky Hands: Puzzling Logic

Guidelines:

  • Yes, this is a puzzle.
  • No, there is no prize for getting it right, other than a bit of satisfaction and perhaps even a new way of looking at the world (no joke).
  • If you have questions or think you know the answer, post them in a reply and I will respond as I see fit.
  • PLEASE put "solution" in the message subject if you are posting a solution.
  • If nobody gets it soon, I'll post the solution.
  • If I've already talked to you about a puzzle similar to this, then please don't spoil it for anybody else.

A little old man with good teeth but shaky hands stops you in the street and shows you a game. He tells you that for five dollars, he'll let you play the game fifteen times. If you can win the game at least nine times, and can explain how you did it, he will give you back your five dollars and give you the puzzle for your very own.

You look at the puzzle. There is a small wooden board, and sitting on the board are four walnut shells and a pebble. The idea seems fairly clear.

"Why would I want to win this silly game, old man?" you ask. "Because it's magic, and also because the game can only be won by the worthy."

"The worthy? How does one play?"

He refuses to explain any further without the money. You can take a chance, or move on down the road. Flush with cash from the sale of your old Jimi Hendrix LP's on eBay, you decide to play.

Now the old man explains that he will put the pebble under one of the four shells. The game, however, is magical: after he has put it under one shell and said the magic words, "Lah Eetnom!," it will randomly transport to one of the other shells, so neither of you can know where the pebble is hiding. You will choose a shell by placing your finger on it.

You interrupt. "This isn't fair! With a 25% chance of winning, I'll never be able to win nine times!" (Generations will wonder why you chose to argue this point, instead of calling Bellevue when he told you the game was magic. It's good you didn't, though, as you'll soon see.)

The old man chastises you for interrupting, and continues to explain. What is under the shell you pick is not immediately revealed. Instead, two other shells will immediately flip themselves over, revealing that they are empty. Finally, you have a choice: stick with your original shell, or switch to the remaining shell which has not yet been disturbed. You win the game if the pebble is under your final choice.

"Are there any tricks? How do I know the pebble isn't going to switch away from whatever shell I choose?" You apparently have some "trust issues," but the old man is used to this question. He explains that he is not in control of the game, and the pebble only jumps, at most, once per game (it will sometimes stay under the original shell). There are no tricks.

With a smile on your face, you play the first round, confident of your win.

A few minutes later, after winning a full eleven out of the fifteen rounds, the old man asks you to explain your winning strategy, and you oblige. He hands back your five dollars and gives you the game.

"You've proven your worthiness, but I'm sorry to say that this game comes with a curse. You must show it to everyone you meet, and can only rid yourself of it as I have just done: someone must play the game fifteen times, win at least nine, and explain how they did it."

With a wink and a nod, the man vanishes.

Here, of course, is the puzzle. Explain how you knew how to win. Tell us what you did, and why. What were your odds of winning each round?

Page last updated: 11/6/2004




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