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?

(In reply to Where is this wrong? by Amber)

Amber wrote: "Ethan agrees that Dan is a liar, so Ethan is not a liar. We already have two Knights (Cory and Beth), so Ethan must be a Knave. Ethan tells the truth with his second sentence ("I'm not a Liar but Dan is"), so to alternate he has to lie when he says the colour is "not green". Therefore the colour must be green, Cory has lied, and therefore so has Beth."

Here's where this is wrong. What Ethan actually says is "No, it's either red or purple, not green." This is an (implied) AND statement: "(It's either red or purple) AND (it's not green)". For an AND statement to be false, it's only necessary for either part joined by the AND to be false. In this case the left side, "it's either red or purple", is false, since the true color of the antidote is yellow. So the whole statement is false. Therefore Knave Ethan told a lie ("No, it's either red or purple, not green"), a truth ( "No, I'm not [a Liar], but you [Dan] are") and a lie ("No, it's none of those [yellow, green or red].") 

The antidote is yellow. Ethan and Abe are Knaves, Dan and Fred are Liars, and Beth and Cory are Knights.

 

 

 

 

Edited on May 31, 2005, 11:56 am

Posted by Penny on 2005-05-31 04:39:56