Four Airmen, Four Posts - and a Redundant Clue
Four airmen - Ahmed, Bilal, Chen and Danish - must be posted one each to four posts: Gate, Tower, Stores and Motor Pool. The duty officer issues these constraints:
- Chen is posted to the Gate.
- Bilal is posted to either the Tower or the Stores.
- Danish is not posted to the Tower.
- Danish is not posted to the Motor Pool.
Shortly before the roster is published, a visiting officer reads the constraints and announces, as though it were new information, "Danish is certainly not on the Tower." The duty officer is unsure whether the visiting officer is adding a fifth rule or merely repeating one of the four.
1. Is the visiting officer's statement new information? Answer precisely, and explain what a statement has to do to be worth acting on.
Read the worked answer
No - it is already entailed. Constraint 3 says in terms that Danish is not posted to the Tower. The visiting officer has not merely repeated a rule; he has restated one of the four constraints almost word for word. It adds nothing to the roster and nothing to the reasoning.
The stronger point. Even if constraint 3 had never been written, the conclusion would still follow. Step 2 of the derivation shows Danish at Stores, and Stores is not the Tower. So "Danish is not on the Tower" is a consequence of the other constraints as well as an explicit rule. It is redundant twice over.
What a useful new statement looks like. To change the roster, a statement must eliminate a possibility that is still live after the current constraints. After the derivation, nothing is live. Any further "rule" of the form "X is not at Y" must therefore be either true of the fixed solution (redundant, as here) or false of it - and a false rule does not refine the roster, it contradicts it.
Judgement. The correct response is not to add a fifth rule to the board but to ask whether the visiting officer believes one of the existing four is wrong. Treating a restatement as new input invites a phantom constraint that later appears to "conflict" with the others.
2. The duty officer now proposes to move Bilal to the Motor Pool. What follows, and how should the proposal be handled?
Read the worked answer
Check it against the constraints. Bilal is currently at the Tower under constraint 2, which requires him to be at the Tower or the Stores. Motor Pool is neither. The move therefore violates constraint 2 outright - it is not a matter of re-deriving around it.
If command authorises it anyway, the roster is rebuilt by elimination:
- Chen = Gate (constraint 1 stands)
- Danish = Stores (constraints 3 and 4 still force this)
- Bilal = Motor Pool (the authorised change)
- Ahmed = Tower - the only post left
Every other constraint survives: Danish is still at neither Tower nor Motor Pool. The single forced consequence is Ahmed moving from Motor Pool to Tower.
How to handle it. Do not publish it as a routine adjustment. Say plainly that the move is inconsistent with a written constraint, name the constraint, state the only knock-on effect (Ahmed to Tower, with any Tower-specific qualification that implies), and ask for amendment of constraint 2 in writing. A roster that quietly contradicts its own stated rule is how the next duty officer ends up rebuilding it from scratch.