### Brain Teasers

# Friends and a Wallet

You and your five friends, conveniently named A, B, C, D, and E, were hanging out when you spotted a wallet on the floor. You have a poor memory, but you remember that it is owned by one of your friends.

You: Whose wallet is this?

A: That's mine.

D: You're lying, A.

C: Yeah, A, you are lying.

B: A is not lying, guys.

D: That wallet is owned by C.

E: Yeah, D is telling the truth.

B: No, E. That's your wallet.

You remember that at least 2 of your friends always tell the truth (truthtellers), while at least 2 always lie (liars).

Thanks to your memory, however, you can't remember which friend lies or tells the truth.

Can you figure out who owns the wallet?

You: Whose wallet is this?

A: That's mine.

D: You're lying, A.

C: Yeah, A, you are lying.

B: A is not lying, guys.

D: That wallet is owned by C.

E: Yeah, D is telling the truth.

B: No, E. That's your wallet.

You remember that at least 2 of your friends always tell the truth (truthtellers), while at least 2 always lie (liars).

Thanks to your memory, however, you can't remember which friend lies or tells the truth.

Can you figure out who owns the wallet?

### Answer

C owns the wallet.EXPLANATION:

B's first statement says that A is telling the truth that it is A's wallet. His second statement, however, says that it is E's wallet. The statements cannot be true at the same time, so B lied in both of them. B is a liar.

Since B was lying when he said that A is telling the truth, A is the other liar, too.

C and D are automatically truthtellers, since they both told the truth when they said A was lying. E is also a truthteller since he said that D told the truth.

Therefore, C owns the wallet.

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## Comments

this was an easy one

If some always told the truth, and some always lied -- I'd just ask each of them a simple question that I knew the answer to and see who answered truthfully.

Hmm... hehe. Never thought of that.

I agree with the conclusion, of course - but this kind of puzzle statement ("at least two.....") leaves open one more possibility that could complicate things. The fifth person can be any of three things - a truthteller, a liar, or someone that does a little of each! That third possibility has to be considered.

Still, it looks like "C" is the only logical choice in this one.

Still, it looks like "C" is the only logical choice in this one.

Oops. I should've written "you're friends are either truthtellers or liars", to get rif of that third option.

Thanks for the comment!

Thanks for the comment!

Fun, and hard.

Yeh, P're! Galing ah!

Fun. Never that easy, never that hard. Just at the midway.

Fun. Never that easy, never that hard. Just at the midway.

YES! The first (actually hard) Logic puzzle I have gotten!

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