Home > Logic > Liars and Knights
| Three guys, a girl, and a fork. (Posted on 2003-09-03) |
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You are walking to a destination, and have to pass through Talking Town. As is common with these problems, you see a fork in the road, and inquire about which way leads to Truth Town. Four people around give you advice, but you don't know their veracity or their gender. You gather from their conversation that all four are either knights or liars, and there is exactly one girl in the group.
A: Take the left fork to get to Truth Town.
B: All liars are girls.
C: All knights are girls.
D: All people who begin their statments with "All" are either all knights or all liars.
Just from these four statements, can you see whether the left or right fork leads to Truth Town? (Also: Which one is the girl?)
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Submitted by Gamer
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Rating: 3.1429 (7 votes)
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Solution:
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You can figure that the right fork leads to Truth Town, and that C is the girl.
You know that the liars and knights combined is 4. Since there is only one girl among them, B and C can't both be knights. Therefore, D can't be a knight, because then both B and C would be knights. Since D is a liar, both B and C can't be liars, or D would be a knight. (because all three of them are liars)
Since there are 2 liars already ((B or C) and D), you know B has to be a liar, as there can't be two (or more) girls.
This means that C is a knight, and all knights are girls. So C is a girl, and since there is only one girl, A must be a liar (because if he was a knight, he would be a girl, and there would be more than one girl.) This means that the right fork leads to Truth Town. |
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