You are an apprentice at Hyperlogitech Corp. The first thing you learn is every department at Hyperlogitech Corp. has two managers, one of the managers is a Knight, and the other is a Liar. At the first board meeting you attend you ask the managers which department they work for. The responses are as follows:

Fiona: None of Alice, Carol and Eddy are in production.
Alice: Carol is in accounting.
Carol: Eddy and I are in the same department.
Bert:  Dave is the Liar from accounting.
Carol: Fiona is in accounting.
Dave:  At most one of Alice, Carol and Eddy is a liar.
Eddy:  Bert and I are in different departments.
Alice: Fiona is in shipping.

Which managers are in charge of which departments and who are the knights and who are the liars?

First, Alice and Carol both say something about which department Fiona is in, but they say different things. Therefore at least one of them is a Liar.

If Alice and Carol are both Liars, then Fiona must be in Production, and also there is only one more Liar out there. Well, Dave’s statement is a lie, because both Alice and Carol are Liars, so that’s more that his "at most one…" So no one else can be lying under this assumption. Bert’s statement would then be true, and Dave is a Liar, as we said, and in accounting. Fiona must be telling the truth, so Carol must in shipping (since Alice lied saying Carol was in accounting). Since Alice is the third Liar, she must be in a different dept from Carol and Dave, so she must be in production. But Fiona say’s Alice isn’t in production. This is a contradiction!

Therefore exactly one of Alice and Carol is a Liar and exactly one is a Knight.

This means that if Dave is a Knight, then so is Eddy in order for Dave’s statement to indeed be true. Also, if Dave is a Liar, then so is Eddy for the same reason.

Ok, so let’s assume Dave is a Liar. Then Eddy is a Liar too. Since one of Alice and Carol is a Liar, this means that Bert and Fiona must be Knights. Since Eddy’s statement is actually a lie, this means that he and Bert actually are in the same department, and since Bert is a Knight there is no contradiction yet. Since Bert’s statement is true, this means that Eddy can’t be in accounting since that Liar spot is taken by Dave. Also, Fiona truthfully says that Eddy is not in production. Therefore Eddy is in Shipping, and so is Bert. Fiona’s statement also says that Alice and Carol aren’t in production. Neither can be in shipping since that is all taken by Bert and Eddy, they must both be in Accounting. But Dave is in accounting. Contradiction! Therefore assuming Dave and Eddy are liars was incorrect.

Therefore Dave is a Knight, which means Eddy is a Knight too. Since one of Alice and Carol is a Knight, this means that Bert and Fiona must be Liars. Carol says that she and Eddy are in the same department – if this is true then she is a Knight, but so is Eddy. Two Knights can’t be in the same department. Therefore Carol is the Liar, and Alice is the Knight.

From this it follows that Carol is in Accounting, and Fiona is in Shipping. Therefore the third Liar, Bert, must be in Production. Since Eddy says he is not in production with Bert, and Carol is not in production, this means that Alice must be in Production in order for Fiona’s statement to be false. By Carol’s statement, we know that Eddy is not in accounting with her, and we already said he wasn’t in production, so Eddy is in Shipping. This leaves Dave in accounting.

So we have:

Alice is a Knight and Bert is a Liar. They are in charge of Production.
Dave is a Knight and Carol is a Liar. They are in charge of Accounting.
Eddy is a Knight and Fiona is a Liar. They are in charge of Shipping.

And no contradictions!

Posted by nikki on 2004-11-01 16:04:25