Case 49 · truth-count deduction · Medium · About 5-10 minutes
A brass compass is hidden in one of five closed drawers. Above the drawers are five statements. A single reliable note says that exactly two statements are true. That is the entire trick: no witness changes their story, and no drawer is secretly empty and full at once.
Read the plaques as statements about the compass’s location. The letter on a plaque names the plaque, not necessarily the drawer it describes.
Five plaques, one compass
The drawers are A, B, C, D, and E. Exactly one drawer contains the compass. All other drawers are empty. The five statements are:
- Plaque A: The compass is in drawer A or drawer B.
- Plaque B: The compass is not in drawer C.
- Plaque C: The compass is in drawer D or drawer E.
- Plaque D: The compass is in drawer A.
- Plaque E: The compass is not in drawer E.
The separate note guarantees that exactly two of those five statements are true. Every other statement is false. “Or” has its ordinary inclusive meaning; with only one compass, both named drawers cannot contain it anyway.
Which drawer should you open? Give the drawer and identify its two true plaques. Then show why no other drawer fits the note.
You can solve by testing the five possible locations. Keep the candidate location fixed while evaluating all five plaques. Do not decide that a plaque is true merely because it is attached to the right drawer.
Hint 1 - reveal when you want a nudge
There are five candidate locations, not five independent hidden objects. Test one candidate at a time.
Hint 2 - reveal when you want a nudge
If the compass is in E, both negative statements need careful reading: “not in C” is true, but “not in E” is false.
Reveal the solution and explanation
Open drawer E. Plaques B and C are the two true statements.
With the compass in E, plaque A is false because neither A nor B contains it. Plaque B is true because E is not C. Plaque C is true because the compass is in one of D or E. Plaque D is false because A is empty. Plaque E is false because the compass really is in E. The total is exactly two.
Testing the remaining locations proves uniqueness. In A, plaques A, B, D, and E are true, for a total of four. In B, A, B, and E are true, for three. In C, only E is true, for one. In D, B, C, and E are true, for three. None gives two.
The lesson is a useful one for statement puzzles: evaluate claims against a proposed world. Do not assume that a truthful statement must have been placed beside the hidden object. Here the plaque attached to the correct drawer is itself false.
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