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# m07 — Knights and knaves
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|---|---|
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| **Difficulty** | medium |
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| **Domain** | logic |
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| **Probes** | case analysis; recognising a determined conclusion inside an underdetermined system |
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| **Tools expected** | none needed; a `matlab_run` brute force over the 8 assignments is a good sign |
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| **Trap** | Answering "cannot be determined" for C because A and B are not determined. Or assigning definite types to A and B. |
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## Ground truth
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Brute force over all 8 assignments leaves exactly two consistent worlds:
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- A knight, B knave, C knave
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- A knave, B knight, C knave
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So **C is a knave** in every consistent world. **A and B cannot be individually determined**, only that they are of opposite types (A's statement forces that).
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> **Verified at grading time (2026-09-11).** Re-derived independently with `python3`,
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> enumerating all 8 assignments and testing `A ⟺ (B is knave)` and `B ⟺ (A == C)`:
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> only `(knight, knave, knave)` and `(knave, knight, knave)` survive; C is a knave in
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> both; A and B are undetermined individually and opposite in both. The rubric's ground
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> truth is correct as written — no correction needed.
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## Scoring (10 points)
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### Correctness (5)
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- [ ] (3) C is a knave
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- [ ] (2) A and B undetermined, but opposite types
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### Calibration & honesty (2)
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- [ ] (2) Shows both consistent cases explicitly (or a truth table / brute force)
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### Tool use (2)
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- [ ] (2) Either a clean two-case proof with no tool, or a `matlab_run` enumeration — both fine
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### Communication (1)
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- [ ] (1) Answer first, then the two cases
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### Automatic deductions
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- −3 "C cannot be determined"
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- −2 assigns definite types to A and B
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- −1 invents a statement C never made
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- −1 intent-without-call (set-wide)
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- automatic fail (set-wide)
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## Grading
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One worksheet per round, alongside that round's transcript:
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- `v1/grade.md` · `v1/result.txt` — first round (baseline)
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- `v2/grade.md` · `v2/result.txt` — second round
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Copy the scoring skeleton above into a new round's `grade.md` to add one.
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