Four Nights, Seven People, One Broken Rule
You are the adjutant of a territorial army unit preparing a four-night standing patrol exercise. Seven appointments are available: officers O1, O2, O3 and naiks N1, N2, N3, N4. Each night requires one duty officer (DO) and one duty NCO (DNCO); nights 2 and 4 also require a signaller, drawn from the unit's two trained operators, N2 and N4. The restrictions are these. R1: exactly those appointments each night. R2: N1 may be detailed only when O2 is the DO, because of a pending verification. R3: N3 is on light duty up to and including night 2, so no duty on nights 1 and 2. R4: N4 cannot be on duty on consecutive nights. R5: N2 cannot be signaller on night 4, because he must hand over the net log at 0600. R6: no person may hold more than two duties across the four nights. R7: O1 cannot be DO on night 3, as he returns from a course that evening. The roster was approved and published yesterday. At 0900 on day 3, before night 3, two things happen: O2 is admitted to hospital with high fever, and N4 is found with a temperature of 103°F and taken off the exercise.
1. Produce a roster for all four nights that satisfies all seven rules, and show how each rule is checked.
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One valid roster (others exist; the marks are in the checking, not in matching this table):
| Night | DO | DNCO | Signaller |
|---|---|---|---|
| 1 | O1 | N2 | - |
| 2 | O2 | N1 | N4 |
| 3 | O3 | N3 | - |
| 4 | O1 | N3 | N4 |
Duty count: O1 = 2, O2 = 1, O3 = 1, N1 = 1, N2 = 1, N3 = 2, N4 = 2.
Checks: R1 - every night has a DO and a DNCO, and nights 2 and 4 carry a signaller who is N4, an authorised operator. R2 - N1 is detailed only on night 2, where O2 is DO. R3 - N3 appears only on nights 3 and 4. R4 - N4 is on nights 2 and 4, which are not consecutive. R5 - N2 is never signaller. R6 - the maximum is two duties, held by O1, N3 and N4. R7 - O1 is DO on nights 1 and 4, not night 3.
The useful discipline is to build the roster around the tightest constraint first: R3 fixes N3 to nights 3 and 4, R4 and R5 fix the signaller pattern to N4 twice, and R2 then forces the O2/N1 pairing. Everything else falls out.
2. With O2 and N4 gone from 0900 on day 3, show whether nights 3 and 4 can still be filled, and identify the exact rule that blocks it.
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Remaining personnel: O1, O3, N1, N2, N3.
Step 1 - N1 is unusable. R2 permits N1 only with O2 as DO, and O2 is in hospital. That leaves two NCOs, N2 and N3, for two nights of DNCO duty.
Step 2 - the signaller. Night 4 requires a signaller drawn from N2 or N4. N4 is off the exercise, so the only qualified person left is N2 - but R5 forbids N2 as signaller on night 4. There is no third trained operator in the unit list.
Step 3 - everything else is satisfiable. Night 3: O3 as DO (O1 barred by R7), DNCO N2 or N3. Night 4: O1 as DO, the other NCO as DNCO, and N2 as signaller. Duty counts remain within R6: whichever NCO works both nights reaches exactly two, and N2 reaches two if he is both DNCO on night 3 and signaller on night 4.
So the residual is precise and singular: R5 is the only rule that cannot be met. The rest of the plan still closes. This is worth stating in exactly this form, because the fix depends on knowing that one rule, and only one, must be dealt with.
3. Recommend what you do, rank the options with reasons, and state what the deviation record must contain if you relax a rule.
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Options, in order:
- Request a signaller from battalion headquarters (best). It preserves R5, avoids overworking an NCO who may then be on the net for two consecutive nights, and costs one vehicle move. It is only viable because there is lead time: the request goes out before 1300 on day 3, the signaller arrives by 1700, and the net log handover at 0600 is unaffected.
- Waive R5 and use N2 as signaller on night 4, with mitigations (fallback). N2 must then have no other duty on day 4: rest from 1200, no guard, no fatigue duties. The DO takes the radio log at every half-hourly check instead of relying on the signaller, and the night is shortened if the net is quiet. Waiving is defensible because R5 exists to protect the 0600 handover, and a rested N2 who hands over after a quiet night still does that.
- Run night 4 with DO and DNCO only (reject). R1 exists because the net must be manned; saving a rule by breaking the purpose of the exercise is not a solution.
The deviation record must state the date and time of the incident, the rule relaxed and why the alternatives failed, who authorised the relaxation, the mitigations applied, and the fact that battalion was informed.