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?

1stly, Fred is NOT a knight (he contradicts himself in his 2nd statement if so).

Consider Dan's 2nd statement: If Dan is a Knight/truthtelling knave, Then Cory, Abe, Beth, Ethan, are not Knights. => Insufficient Knights! Hence Dan is not truthtelling due to his 2nd statement (ln 5). He must be a liar/knave. If He is a lying liar, Ethan's lying in his 1st statement. If he's a knave, Ethan's lying in his 2nd statement. => Hence Dan and Ethan are NOT knights.

We have Cory, Beth and Abe as potential knights. Since Beth and Abe cannot be knights together (which makes all of them knights), Cory is a knight.

Hence Dan is a liar (as Cory said) and Ethan a knave (could be proved by both his first two statements: 1st statement: NOT green is a fact from Cory, no matter what he say before that).

Now, Cory, Dan, and Ethan are id-ed. Abe and Beth tell truths (about cory is a knight). Hence the missing liar can only be Fred.

Now, as Fred is lying, Black, Green, White, Purple are not the antidote needed. Possible answer: Yellow/Red. Since Ethan's 3rd statement is true (proved by Cory, 'NOT green'), The potion is the RED one. 

O shooot. I couldn't label the ids of Beth and Abe. Am I wrong throughout the way?

Posted by Terence on 2005-10-06 19:06:00