### 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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