Puzzle No. 029
Picarats: 20


Five suspects are called into police headquarters for questioning. They give the following statements,
A: "One of the five of us is lying."
B: "Two of the five of us are lying."
C: "I know these guys, and three of the five of us are lying."
D: "Don't listen to a word they say. Out of the five of us, four are lying."
E. "All five of us are dirty rotten liars!"

The police only want to release the suspects who are telling the truth. How many people should they let go?













Hint One: This puzzle might look like a big mess at first, but it's fairly simple when all is said and done.

Take E, for example, who says everyone is lying. If she is actually telling the truth, then her statement becomes a lie, and she must be ruled out. Yep, E's a liar for sure.

Hint Two: Let's rule out another couple of suspects. If A's statement is true, then three other people should be saying the same thing as A. This is not the case, so A is a liar.

If B is telling the truth, two other suspects should say the same thing as B. Once again, this is not the case, so B must be lying.

Hint Three: So, to sum things up, so far we've proven that A, B, and E are lying. Let's examine the last two suspects.

If three people are lying, the other two suspects should have the same statement, but everyone is saying something different. On the other hand, if four of the five suspects are lying...

Solution:













That's right! Every suspect accused a different number of people. If anyone was telling the truth, it had to be one suspect, no more no less.

The only suspect whose statement fits that condition is D. It looks like he's a free man now.