Hyperlogitech Corp. just discovered that they have two employees embezzling funds. Investigators have narrowed the field down to six suspects.

The suspects are Alice, Bert, Carl, Dave, Emily, and Fiona. In the group there are two Knights, two Knaves and two Liars. (For this puzzle, Knaves alternate truths and lies.)

Each suspect made comments as follows:

Alice: No women are crooks. Emily and Fiona are Liars.

Bert: Alice is a crook, but I am not. One of the women is a Liar.

Carl: Fiona is a crook, but I am not. Dave is a Knight. Fiona is a Knave.

Dave: Emily is a crook, but I am not. Bert is a Liar.

Emily: Alice isn't a Knight. Carl is not a crook.

Fiona: Emily is a Liar. Dave is not a crook.

Who are the embezzlers?

(In reply to Solution + Explanation by nikki)

Hmm, I had attempted to solve this problem without assuming if "So and so is a crook, but I am not" should be considered one or two statements in the case of Liars and Knaves (if it’s a Knight, they both have to be true no matter what). I thought I had done so, until I looked back and noticed I was wrong. I did use an assumption near the end when I said "Since Carl’s statement ‘Dave is a Knight’ is false, this means that ‘Fiona is a crook, but I am not’ is true."

But everything I did before that is ok. Here’s a snapshot of what I found so far:

Alice: Liar and Crook
Bert: Knight, and not a Crook (by his own statements as a Knight)
Carl: Knave, and not a Crook (by Emily’s statements)
Dave: ?
Emily: Knight
Fiona: ?

Well, my arguments for Fiona being a Knave are still true (by Carl's third sentence), which still leaves Dave as a Liar.

We already said Fiona’s first statement is a lie, so her second statement must be true.
So Dave is not a crook.

Since Dave is a Liar, his statement "Emily is a Crook, but I am not" must be a lie.
Since he is not a crook, then the "Emily is a Crook" part must be a lie.
Note: this is not making the same assumption as I started out trying to avoid. I have shown by other ways that the second half of that statement was true, and since he is a liar the whole statement can’t be true. Therefore the first half is a lie.

So Emily is not a Crook.
So the only person left who can be a Crook is Fiona.

Posted by nikki on 2004-10-11 19:35:50