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?

The biggest lead I saw was that both Alice and Fiona make comments about Emily being a liar. So I'm going to start there.

Assume "Emily and Fiona are Liars" is a true statement.
Then Fiona's statement "Emily is a Liar" must be a lie.
But Emily is a Liar, so we have a contradiction.

Therefore, "Emily and Fiona are Liars" is a false statement.
This means that both Emily and Fiona can't be Liars, but one of them could be.
Also, Alice cannot be a Knight since she told at least one lie.
This means that Emily's statement "Alice isn't a Knight" is true.
Therefore Emily cannot be a Liar.
This means "Emily is a Liar" is a false statement.
Therefore Fiona cannot be a Knight.

Next, let's assume that "Dave is a Knight" is a true statement.
Then Carl can't be a Liar since he says that statement.
So Dave's statement "Bert is a Liar" is true.
But then Bert's statement "One of the women is a Liar" is actually true.
Why? Because Carl and Dave can't be Liars, which means that one of the women must be a Liar with Bert.
So we have a contradiction.

Therefore, "Dave is a Knight" is a false statement.
So Carl cannot be a Knight, since he told at least one lie.

Well, we've named 4 people who can't be knights (Alice, Fiona, Dave, and Carl).
Therefore Bert and Emily are Knights.

By Bert's statements, this means that Alice is a Crook.
Which means that Alice's statement "No women are crooks" is a lie.
Since we've shown both of her statements to be lies, we know that Alice is a Liar.

Next up, since we know Carl can't be a Knight, let's see if he's a Liar.
Assume Carl is a Liar.
Then Fiona is not a knave. We already determined she couldn't be a Knight.
Therefore Fiona is a Liar.
But now we have three Liars (Alice, Carl, and Fiona).

Therefore, Carl can't be a Liar. So Carl must be a Knave.
Since Carl's statement "Dave is a Knight" is false, this means that "Fiona is a crook, but I am not" is true.
So Fiona is the other Crook.

So the answer to the problem's question is that Alice and Fiona are the two crooks.

But for completeness, here is what everyone else is:
Since Carl is a Knave and "Dave is a Knight" is false, this means that "Fiona is a Knave" is true.
So Fiona is a Knave.

This means Dave is the other Liar. So…

Alice: Liar and Crook
Bert: Knight
Carl: Knave
Dave: Liar
Emily: Knight
Fiona: Knave and Crook

And there are no contradictions!

fixing typos. Please see another post for a solution without a certain assumption

Edited on October 11, 2004, 7:26 pm

Posted by nikki on 2004-10-11 19:04:02