Puzzle | The Stolen Necklace

A priceless necklace has been stolen from a mansion, and the police have narrowed it down to three suspects: Alice, Bob, and Carol. The detective on the case interrogates them and gets the following statements:

Alice: “I didn’t do it! Bob is lying.”

Bob: “I didn’t do it! Carol is lying.”

Carol: “I didn’t do it! Bob and Alice are both lying.”

The detective knows that exactly one of the three suspects is the thief and that the other two are telling the truth. Who stole the necklace?

Can you use logic to determine which of the three suspects is the thief based on their statements?

Puzzle | The Stolen Necklace

Solution:

• Alice: “I didn’t do it! Bob is lying.”

If Alice is telling the truth, it means Bob is lying, which implies that either Bob or Carol is the thief.

• Bob: “I didn’t do it! Carol is lying.”

If Bob is telling the truth, it means Carol is lying, which implies that either Alice or Carol is the thief.

• Carol: “I didn’t do it! Bob and Alice are both lying.”

If Carol is telling the truth, it means both Bob and Alice are lying, which implies that either Alice or Bob is the thief.

let’s consider the possibilities:

• If Alice is the thief:

Alice is lying about being innocent, but Bob’s statement “Carol is lying” would also be true. This would contradict the rule that only one person is lying.

• If Bob is the thief:

Bob is lying about being innocent, but Carol’s statement “Bob and Alice are both lying” would also be true. This would contradict the rule that only one person is lying.

• If Carol is the thief:

Carol is lying about being innocent, and both Alice and Bob are telling the truth, which is consistent with the rule that only one person is lying.

Based on this analysis, it appears that Carol is the thief. Her statement contradicts the rule that only one person is lying, while the statements of Alice and Bob are consistent with the rule that two people are telling the truth. Therefore, Carol stole the necklace.