The Hardest Logic Puzzle Ever

There's a classic logic puzzle in which a person must take a fork in the road, one of which is safe, but the other is a deadly trap. Two men guard the fork, one of which always lies, but the other always tells the truth. The person gets to ask one question in order to determine which path is the safe one.

Mathematician Raymond Smullyan has added another dimension to this puzzle. See if you can figure it out:

There are three guardians, A, B and C. Their names are Knight, Knave and Chaos. Knight always speaks truly, Knave always lies. Chaos tossed a coin this morning to decide whether today he would behave like Knight or like Knave.

Your task is simple: ask three yes-no questions, each of a single guardian, and determine which is Knight, which is Knave, and which is Chaos. There is, alas, a complication: the guardians understand English but will answer in the local language, in which “Da” means yes and “Ja” means no. Or possibly “Ja” means yes and “Da” means no – you cannot remember.


Link via Marginal Revolution | Raymond Smullyan

UPDATE 3/18/10: Here's the solution.

Comments (39)

Newest 5
Newest 5 Comments

Very Easy... Ask one of them it does not matter weather he is a knight or a knave. Ask "what will you say if the other guard will point the correct path?" if the guard you asked answered "the left" go to the right.. if he answered "the right" go to left.. simple...
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Ask Guardian A, “If I asked you, “Are you Chaos?” in your current mental state, would you say “ja”?”
If A answers “ja”, he’s Chaos. Then ask Guardian B, “If I asked you, “Are you Knight?”, would you say “ja”?”. The answer is “ja” if B is Knight, and either way the problem is now solved.

If A answers “da”, he’s either Knight or Knave. So ask him instead, “If I asked you, “Are you Knight?”, would you say “ja”?” If the answer is “ja” he’s Knight; otherwise he is Knave.
So, now, ask him “If I asked you, “Is guardian B Chaos”, would you say “ja”?” If he answers “ja”, B is Chaos, and C is the opposite of A. If he answers “da” then C is Chaos and B is the opposite of A.
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How typically American and pedantic to make light of a serious thing.
Yeah it's important to have a sense of humor, but really, isn't this rather childish? How are you going to explain this to the kids? Oh, they'll remember this moment, when the whole town's signs went silly. They'll remember.
And the drunk drivers will be saying "Oh, I thought they were joke signs, not really serious about us actually reading them and understanding that they're not jokes."
Nice.
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we can only hope. anyway we have people who spraypaint HAMMERTIME under the stop on the signs in madison. pretty amusing, actually. the city doesn't bother to pay people to clean it off cause there haven't been any complaints yet.
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Seriously, if they took the money from this project and just had a police presence every once in a while giving out tickets to violators at these intersections they'd save money, lives, and make a more effective statement.

It's fine to take it lightly, but a cop showing up even every now and again gets the message across pretty quick "don't cruise through this stop sign". And if that doesn't quite work the cost of the ticket for a moving violation as well as the added points to your insurance will speak volumes.
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Ey, weeks ago I was thinking about write "in the name of love" in the signals to make everybody think: "I hate that song" and pass away.

I´m not liying...
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I see a multitude of problems with this as well. I see people taking the signs less seriously and I doubt those who roll through stop signs fail to see the sign in the first place. Seems like a waste of time and money if this was intended as a serious campaign. The money would have been better spent in patrolling and driving re-education.

If was done just for the fun of it though, then I'm for it.
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I think it's a rather clever solution that will get the stop signs a bit more attention while not adding ill will towards cops as an overbearing cruiser presence might.
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@k

dude, when every pompously official-sounding message of government already has the credibility of an arsonist giving fire-safety tips, you oughta think about the benefits of cutting through the clutter to reclaim some little bit of attention. Or you could just take a breath and take what seems like a much-needed vacation.
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Got to agree with the nay-sayers. Who cares about creating ill-will towards the police? They're there to ticket people who aren't obeying the law.

And the possibility of people interpreting the stop signs themselves as fakes is too big a risk to take with people's lives.

"I'm sorry I ran over your daughter, but isn't that a funny sign?"
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