Home > Logic > Liars and Knights
| Find the Antidote (Posted on 2005-05-20) |
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You're in the middle of a long hike through the jungle when you're bitten by a venomous snake. You run to the nearest building you can find, which, lucky for you, happens to be the local witch doctor's. Unfortunately, the witch doctor is out. His six assistants--Abe, Beth, Cory, Dan, Ethan and Fred--are there, however. It is known that two of them are knights, two are knaves and two are liars.
You see that there are six differently colored potions sitting a shelf marked "snake-bite antidotes"--red, yellow, green, black, purple and white--and you describe the snake that bit you and ask which potion you should take. The following conversation ensues:
Fred: "Oh, of course--it's the black one or the white one."
Abe: "It's either black, yellow or purple, or Fred is a liar...but not both."
Ethan: "No, it's either red or purple, not green."
Dan: "Ethan, you're a liar."
Ethan: "No, I'm not, but you are."
Dan: "OK, well, if I'm a liar, then you're right, it's red or purple."
Cory: "You are a liar--I'm not, though."
Abe: "Yeah, Cory or Fred is a knight."
Fred: "Personally, I'm a knave, and it's either the green, white or purple."
Beth: "No, it's either the yellow, green or red."
Ethan: "No, it's none of those."
Cory: "It's yellow, white or red, not green."
Beth: "I guess you should listen to Cory--he's a knight."
Who's what? And which potion should you take?
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Submitted by yocko
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Rating: 4.2857 (7 votes)
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Solution:
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Assume Ethan is a knight. Then, from his first and third statements, we know the correct potion is purple. Fred's first statement, Dan's first, Cory's second, Beth's second, and Abe's second statement are all false, which means none of them could be knights, and we know that of these five, one must be a knight. So we know Ethan could not be a knight. Assuming Ethan is a liar, Fred's first statement, Cory's first, Abe's second, and Beth's second are all false, again resulting in not enough knights. So Ethan must be a knave.
If Ethan's first and third statements are true, the potion must be purple, and the same contradiction occurs as when we assumed Ethan was a knight. Therefore, we know Ethan's first and third statements are false, and his second statement is true.
So we know that Dan is a liar and the potion must be yellow or blue. Assuming the correct potion is blue, Cory's second statement is false, which means Beth's is too, but her first statement we know to be true, which makes her a knave and Cory a liar (because there would already be two knaves). Therefore, Abe and Fred must both be knights, but Abe's first statement is a lie, a contradiction. So the correct potion to drink is yellow.
This makes Cory's second statement true, which makes his first one true as well, making him a knight. This makes both of Beth's statements true, so she is a knight as well. Abe's second statement is true, so he must be the second knave (because there are already two knights), making Fred the second liar.
In summary:
Abe--knave
Beth--knight
Cory--knight
Dan--liar
Ethan--knave
Fred--liar
The correct potion to drink is yellow. |
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