Five-Post Roster with Overlapping Restrictions
At a rural police station in Sabarkantha, the station officer must post five constables - Amit, Bhavna, Chetan, Divya and Eshan - to five duties for the coming week: Beat North (BN), Beat South (BS), Checkpost (CP), Lockup (LK) and Reserve (RS). Each constable gets exactly one duty. The local rules are: LK must be staffed by a woman constable; only Bhavna and Divya are women. CP requires the sole certified constable, Chetan. BN requires a constable who speaks the local Bhili dialect; only Amit and Eshan speak it, but Amit has a knee injury and is medically barred from BN's long foot route. BS requires at least two years' field experience; Bhavna, Chetan and Eshan meet this, while Divya does not. The officer claims there is only one valid posting plan.
1. Determine the only valid posting for each constable. Show the deduction chain rather than just the final list.
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Start with the fixed posts. CP must be Chetan because he is the only certified constable.
BN must be Amit or Eshan; Amit is medically barred from BN's foot route, so BN = Eshan.
BS needs two years' experience. The eligible constables are Bhavna, Chetan and Eshan, but Chetan and Eshan are already placed, so BS = Bhavna.
LK needs a woman. The women are Bhavna and Divya, and Bhavna is already on BS, so LK = Divya.
The only person left is Amit, so RS = Amit.
The unique roster is: CP - Chetan; BN - Eshan; BS - Bhavna; LK - Divya; RS - Amit.
2. Eshan reports sick. The station officer says the roster can still be filled without violating any rule. Is he correct? If not, identify the conflict and the minimum change needed.
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He is not correct. Without Eshan, BN must go to Amit because Amit is the only remaining Bhili speaker. But Amit's medical restriction bars him from BN's long foot route. The rules now contradict each other, so no valid roster exists.
The minimum change is to relax one restriction. The safer option is to relax Amit's restriction with a written light-duty accommodation: vehicle patrol instead of the foot route, plus a Bhili-speaking liaison. This preserves the language requirement and changes only one rule. The alternative is to relax BN's language requirement and post a non-Bhili speaker with a translator, but that weakens local communication. Either way, the officer's claim is wrong unless one rule is formally changed.
3. A visiting officer suggests swapping Bhavna to LK and Divya to BS. Evaluate the suggestion against the stated rules.
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The swap is invalid. Bhavna can legally take LK because LK requires a woman and she is a woman. But Divya cannot take BS because BS requires at least two years' field experience, and Divya does not meet that requirement. A valid swap would need both postings to satisfy their rules; here only one does. Unless the experience rule is waived in writing, the original roster remains the only valid plan.