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          "title": "Deep Reasoning: Logic Paradoxes & Probability",
          "text": "Six hard reasoning problems: Russell's paradox, Monty Hall, Blue Eyes, Unexpected Exam, Two-Envelope, Sleeping Beauty.\n\nThese require genuine deductive reasoning beyond pattern matching \u2014 they are unlikely to appear verbatim in training data.\n\nJudge scores: 5 = correct with full explanation, 1 = wrong or confabulated.",
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              "problem": "No barber shaves himself",
              "question": "A barber shaves all those, and only those, who do not shave themselves. Does the barber shave himself?",
              "expected": "paradox \u2014 no consistent answer exists (Russell's paradox)"
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              "problem": "Monty Hall",
              "question": "You pick door 1. Host opens door 3 (goat). Should you switch to door 2? Why?",
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              "problem": "Blue eyes",
              "question": "100 logicians on an island all have blue eyes but don't know their own. A stranger says 'I see at least one person with blue eyes.' What happens and why?",
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              "question": "A teacher says: 'There will be a surprise exam next week, you won't know the day until I announce it.' A student argues the exam is impossible. Is the student's logic correct?",
              "expected": "the student's backward induction is flawed \u2014 the paradox shows limits of purely deductive self-reference"
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              "question": "Two envelopes contain money; one has twice the other. You pick one and see \u00a3100. Should you switch? Formalize the paradox.",
              "expected": "the switch argument is flawed \u2014 expected value calculation assumes fixed reference point incorrectly; true expected value is equal"
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              "problem": "Sleeping Beauty",
              "question": "Sleeping Beauty is woken Monday always, and Monday+Tuesday if coin is tails. She has no memory. When woken, what probability should she assign to the coin being heads?",
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