Roster Locked by Five Rules
A sub-inspector must finalise the night picket roster for Monday to Thursday, exactly one constable per night, from four constables: Amit, Bina, Chandan and Deepa. Five conditions apply. (i) Chandan is the only constable trained on the new e-beat reporting app and must be posted on Tuesday for the app audit. (ii) Deepa is on light duty after a knee injury and cannot take Monday, the longest round. (iii) Amit and Bina quarrelled publicly last month; the SHO's written order says they must not be posted on consecutive nights. (iv) Bina must be posted later in the week than Amit, so that she can verify the entries he makes. (v) Chandan and Deepa must not be posted on consecutive nights, because the e-beat handover demonstration needs one night's gap between them. The SHO now telephones to say Chandan's app training has been shifted to Wednesday, and the roster must be rebuilt for that week only.
1. Build the valid roster for the original conditions and show why no other arrangement survives.
Read the worked answer
Fix Chandan = Tuesday from rule (i). The remaining nights are Monday, Wednesday and Thursday for Amit, Bina and Deepa.
Rule (ii) removes Monday for Deepa, so Deepa is Wednesday or Thursday.
Branch 1 - Deepa on Wednesday. Then Amit and Bina take Monday and Thursday, and rule (iv) forces Amit Monday and Bina Thursday. Check rules: (iii) Amit and Bina on Monday and Thursday are not consecutive, so that passes; but (v) Chandan (Tuesday) and Deepa (Wednesday) are consecutive, so this branch fails.
Branch 2 - Deepa on Thursday. Then Amit and Bina take Monday and Wednesday, and rule (iv) forces Amit Monday and Bina Wednesday. Rule (iii): Monday and Wednesday are not consecutive, passes. Rule (v): Tuesday and Thursday are not consecutive, passes.
Valid roster: Monday Amit, Tuesday Chandan, Wednesday Bina, Thursday Deepa. Only one arrangement survives, because every other placement breaks either the non-consecutive order or the 'Bina after Amit' order.
2. With Chandan now fixed on Wednesday, can the roster be rebuilt at all? Show your reasoning.
Read the worked answer
Fix Chandan = Wednesday. Monday, Tuesday and Thursday remain for Amit, Bina and Deepa.
Rule (ii) bars Deepa from Monday, so Deepa is Tuesday or Thursday.
Rule (v) bars Deepa from Tuesday, because Tuesday would be consecutive with Chandan's Wednesday. So Deepa = Thursday.
Amit and Bina are then left with Monday and Tuesday, and rule (iv) forces Amit Monday and Bina Tuesday.
Check rule (iii): Monday and Tuesday are consecutive, so Amit and Bina would be posted back to back. That is precisely what the SHO's written order forbids.
Conclusion: no valid roster exists for that week under all five conditions. The sub-inspector must not silently drop a rule; the file must record which condition failed and why, because the failure is structural (only four nights, one fixed night, one barred night) and not a clerical slip.
3. The SHO insists on Wednesday. Which condition should be relaxed, and how would you record and justify the choice?
Read the worked answer
Rank the conditions by the harm of breaching them. Rule (iii) is a written order made after a public quarrel; breaching it risks an on-duty confrontation and is a discipline issue. Rule (i) is the SHO's own instruction. Rule (iv) is procedural. Rule (v) exists only to stage a training demonstration.
The least damaging relaxation is rule (v): post Deepa on Tuesday and Chandan on Wednesday, and let the e-beat handover be demonstrated by a short video call or by moving the demonstration to the following week. That gives Monday Amit, Tuesday Deepa, Wednesday Chandan, Thursday Bina. Check: Amit and Bina on Monday and Thursday are not consecutive, so rule (iii) holds; Bina is later than Amit, so rule (iv) holds; Deepa is not on Monday, so rule (ii) holds.
The station diary entry should record the date and time of the oral order, that the original roster was found impossible under all five conditions, that rule (v) alone was relaxed, and the reason. The judgment tested is that when constraints conflict, you protect safety and discipline first and re-engineer whatever is merely procedural.