Four Nights, Five Nurses, One Calling in Sick
Four consecutive nights, Monday to Thursday, must each be covered by one nurse as night in-charge on a 20:00–08:00 shift. Five staff are available: Anita, Bilal, Chitra, Deepak and Esha. Exactly one of them is off-duty for the whole block. Ward rules are fixed: Anita cannot take Monday or Thursday because she must present the handover audit at 06:00 on Friday morning; Bilal can only work the night immediately after a night worked by Chitra, because they share the two-person insulin-safety check and the ward will not release the pair from it; Esha can take only Monday or Tuesday because her study leave begins on Wednesday; and Chitra cannot take Thursday because she is the only nurse signed off on the new chemotherapy spill kit and the spill kit audit falls on Friday. Every other combination is permitted. The ward sister must publish the roster before the Monday morning handover.
1. Work out who covers each night. Show your elimination, not just the final answer.
Read the worked answer
Step 1 - translate rule 2 into positions. Bilal works the night immediately after Chitra, and Chitra cannot take Thursday. So the only possible Chitra–Bilal pairs are (Mon Chitra, Tue Bilal), (Tue Chitra, Wed Bilal) and (Wed Chitra, Thu Bilal).
Step 2 - test each pair.
- Pair at Mon–Tue: Esha must take Monday or Tuesday, and both are now occupied. Rejected.
- Pair at Tue–Wed: Esha is therefore forced to Monday. Anita must then take Tuesday or Wednesday - both occupied. Rejected.
- Pair at Wed–Thu: survives.
Step 3 - fill the rest.
- Chitra takes Wednesday, Bilal takes Thursday.
- Anita cannot take Monday or Thursday, and Wednesday is gone, so Anita takes Tuesday.
- Esha must take Monday or Tuesday; Tuesday is taken, so Esha takes Monday.
- The one person off the block is Deepak.
Published roster: Mon Esha, Tue Anita, Wed Chitra, Thu Bilal. Off: Deepak.
Verification: every rule checked individually - Anita not Mon/Thu; Bilal on the night after Chitra; Esha on Mon; Chitra not Thu. All hold.
Why this is a reasoning question and not a memory question: the first two candidate pairs look plausible and are only eliminated by cross-checking against Esha's and Anita's restrictions. A candidate who tests only one pair will publish an invalid roster.
2. On Monday at 14:00 Esha reports fever and is sent home; she cannot work that night. Rebuild the roster using the remaining four nurses and check it against every rule.
Read the worked answer
Esha is now off, so her Monday/Tuesday restriction no longer constrains anything, but Monday must still be filled from Anita, Bilal, Chitra and Deepak.
Step 1 - Monday cannot be Anita. She is barred from Monday by the Friday audit rule. So Monday is Chitra or Deepak.
Step 2 - try Monday = Deepak. Then Chitra and Bilal must occupy Tuesday and Wednesday (their only surviving adjacency), which leaves Thursday for Anita - barred. Dead end.
Step 3 - try Monday = Chitra. Bilal must then take Tuesday. Anita can take Wednesday (not Mon/Thu), leaving Thursday = Deepak and Esha off.
Roster: Mon Chitra, Tue Bilal, Wed Anita, Thu Deepak. Off: Esha.
Rule check: Anita is not on Monday or Thursday ✔. Bilal works the night immediately after Chitra ✔. Chitra is not on Thursday ✔. Esha's restriction is irrelevant while she is off ✔. Exactly one nurse off ✔.
Rest check: Anita's Wednesday night ends 08:00 Thursday; her Friday 06:00 handover audit is 22 hours later, comfortably above the usual 11-hour minimum.
The judgement point: the obvious move - drop Deepak in for Esha and leave everyone else in place - fails, because Esha was holding Monday. The roster has to be re-derived from the constraints, not patched.
3. Anita asks to swap her Tuesday night with Chitra's Wednesday night so she can attend a family function. Test the swap against every rule and decide whether to approve it.
Read the worked answer
Proposed roster after the swap: Mon Esha, Tue Chitra, Wed Anita, Thu Bilal.
Testing rule by rule:
- Anita not Monday or Thursday → Wednesday is permitted ✔
- Esha on Monday or Tuesday → Monday ✔
- Chitra not Thursday → Wednesday ✔
- Bilal must work the night immediately after Chitra → Chitra is Tuesday, Bilal is Thursday. Two nights apart. ✘
The swap must be refused as proposed.
Is there any swap that gives Anita Wednesday off? Anita would then have to work Tuesday or be off. If she takes Tuesday, Chitra and Bilal need an adjacent pair among Wednesday and Thursday - impossible, Chitra cannot take Thursday. If Anita is off, only Chitra, Bilal, Deepak and Esha remain for four nights, and the Chitra–Bilal adjacency plus Esha's Monday–Tuesday limit still collide under the same elimination as before. There is no arrangement: the roster has a unique solution and Wednesday belongs to Chitra.
What to do instead: approve leave for Anita on a different date, or arrange an off-duty swap with Deepak (who is free all week) so that Deepak covers Tuesday and Anita takes an off night - but that changes the pair rule only for Bilal and Chitra, so it must be confirmed with the ward sister who owns the insulin-safety policy, not settled informally between nurses.
The tested judgement: a swap that two nurses have agreed between themselves is not automatically valid. The pair rule exists for patient safety, and one person's convenience never outranks it.