Thursday, October 06, 2005
Your next puzzler -- liars and truth-tellers.
My, but it's been a while since the last puzzle so here's something to keep you occupied. You're travelling down a road in a foreign land, trying to reach the capital city and all you know is that, at some point, you're going to come to a fork in the road and the capital lies down one of those two forks but you have no idea which one.
In addition, you know that the land is occupied by two tribes -- one which always lies and one which always tells the truth. You also know that you can tell them apart since they dress very differently but you have no idea which clothing style matches which tribe.
Eventually, you come to that fork in the road and, lo and behold, there are two natives there just hanging out and dressed differently, so you know one is a liar and the other is a truth-teller -- you just have no idea which one is which.
By asking just a single yes-or-no question of only one of the natives, figure out which fork leads to the capital.
Comments section open for solutions Friday, Oct 7, 6 pm Eastern Time.
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7 comments:
I'm guessing you'd pose the question hypothetically, thusly, "If I were to ask you which road leads to the capital, which road would you point to?"
The truth-teller would point to the correct road. The liar would be forced to lie about the answer he would give, and would have to point to the correct road too.
Philip Torrens
D'oh! Didn't word it quite right. You'd have to ask the question thusly "If I were to ask if this were the road to the captial (indicating one of the two roads), what would you say?" Same logic as per previous post.
Philip T.
I saw something like this in a movie once, I think it was Labrynth. You ask one: 'If I were to ask the other guy if I should take the right fork, what would he say?' With a yes you go left, a No right.
I dunno the answer, but I do know that now matter what it is it will be.....
"Inconceivable!"
Answer: Ask either of the two, "If I asked your counterpart which road to take, which one would he indicate?" Take the other one.
Suppose the capital lies down the right fork.
The truth-teller would tell you this. The liar, being a liar, would tell you that he'd send you down the left fork.
The liar would also send you down the left fork if you asked him directly, so the truth-teller, being a truth-teller, would tell you so honestly.
Thus either one, asked this question, will reliably point down the road that doesn't lead to the capital.
Oh, my mistake. It's phrased in yes-or-no format. The question should then indeed be "If I asked your counterpart whether the left fork led to the capital, would he answer in the affirmative?" Do the opposite of whatever the answer overtly indicates.
If the left fork does lead to the capital, the liar would say "no" and the truth-teller would tell you so, or the truth-teller would say "yes," but the liar would indicate otherwise. Thus a "no" answer always indicates that you arbitrarily picked the correct fork.
If the left fork does not lead to the capital, the liar would say "yes," and the truth-teller would tell you so, or the truth-teller would say "no," but the liar would indicate otherwise. Thus a "yes" answer means you have arbitrarily picked the wrong fork, and you should take the right one instead.
Just ask either one if there are from the left fork. If they both say no then take the right fork and if they both say yes take the left fork. Basically, take any route they say they are from because if they are a truth teller then they will tell you the truth and if they are a liar then they will lie and they they are from the truth land. Either way, you are pointed to the truth land.
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