Daily Math Puzzle: 2026-10-10
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2026-10-10
Inspector Davies is investigating the theft of the priceless 'Serpent's Eye' diamond from Lord Ashworth's study. Four individuals were present: Lord Ashworth's Nephew (Arthur), the Head Butler (Benson), the Housekeeper (Cynthia), and the Visiting Professor (Dr. Evans). Inspector Davies knows one crucial fact: Exactly one of these four is the thief. The thief always lies, and all innocent individuals always tell the absolute truth. Here are their statements: Arthur: "Benson stole the diamond." Benson: "I did not steal the diamond." Cynthia: "Dr. Evans is innocent." Dr. Evans: "Arthur is lying." Who stole the 'Serpent's Eye' diamond?
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Solution
Arthur — Let's analyze each suspect's possibility based on the rule: Exactly one thief, the thief always lies, and the innocent always tell the truth.
1. **Assume Arthur is the thief (and therefore a liar):**
* Arthur says: "Benson stole the diamond." (LIE) -> This means Benson is innocent. (Consistent)
* Benson says: "I did not steal the diamond." (TRUTH, as he's innocent) -> This means Benson is innocent. (Consistent)
* Cynthia says: "Dr. Evans is innocent." (TRUTH, as she's innocent) -> This means Dr. Evans is innocent. (Consistent)
* Dr. Evans says: "Arthur is lying." (TRUTH, as he's innocent) -> This means Arthur is indeed lying. (Consistent, as Arthur is the thief)
* All statements are consistent with Arthur being the thief. This is a possible solution.
2. **Assume Benson is the thief (and therefore a liar):**
* Arthur says: "Benson stole the diamond." (TRUTH, as he's innocent) -> This means Benson is the thief. (Consistent)
* Benson says: "I did not steal the diamond." (LIE, as he's the thief) -> This means Benson is the thief. (Consistent)
* Cynthia says: "Dr. Evans is innocent." (TRUTH, as she's innocent) -> This means Dr. Evans is innocent. (Consistent)
* Dr. Evans says: "Arthur is lying." (TRUTH, as he's innocent) -> This means Arthur is a liar. BUT, if Benson is the thief, Arthur is innocent, and innocent people tell the truth. So Arthur's statement ("Benson stole the diamond") would be true. If Arthur is telling the truth, then Dr. Evans' statement ("Arthur is lying") must be false. But Dr. Evans, being innocent, must tell the truth. This is a **contradiction**.
* Therefore, Benson cannot be the thief.
3. **Assume Cynthia is the thief (and therefore a liar):**
* Cynthia says: "Dr. Evans is innocent." (LIE) -> This means Dr. Evans is the thief. (This is a **contradiction**, as we assumed Cynthia is the thief and there can only be one thief).
* Therefore, Cynthia cannot be the thief.
4. **Assume Dr. Evans is the thief (and therefore a liar):**
* Cynthia says: "Dr. Evans is innocent." (TRUTH, as she's innocent) -> This means Dr. Evans is innocent. (This is a **contradiction**, as we assumed Dr. Evans is the thief).
* Therefore, Dr. Evans cannot be the thief.
Since only the scenario where Arthur is the thief leads to no contradictions, Arthur must be the culprit.
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