Ronda de doze horas: seis cadetes, quatro postos
A detachment of six cadets (A–F) must man four posts - Gate, Hangar, Fuel farm and Tower - continuously for twelve hours, in six duty blocks of two hours. Each cadet may work at most four blocks, and no cadet may work more than two consecutive blocks. Cadet B is unavailable for the first two blocks because of a medical review at 08:00. The Tower must be manned in every block by a cadet holding a radio certificate; A, C and E hold one, and no certificate holder may be posted to the Tower in two consecutive blocks. Separately, the Fuel farm lies 250 m from the Gate and 150 m from the Hangar; a two-person patrol walks at 1,4 m/s and the standing order requires arrival within 90 seconds.
1. Is a roster satisfying all the constraints possible? Justify with a counting argument, not by trial and error.
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Demand: 6 blocks × 4 posts = 24 post-blocks.
Supply from B: B is available only in blocks 3–6. With no more than two consecutive blocks, the largest set B can work is three (e.g. 3, 4, 6 - blocks 3 and 4 are two consecutive, block 6 stands alone). So B contributes at most 3.
Supply from the rest: the other five cadets must cover 24 − 3 = 21 post-blocks, i.e. 4,2 each. But each is capped at 4, giving at most 20.
21 > 20, so the constraints are mutually infeasible: at least one cadet must work five blocks, which the fatigue rule forbids.
Conclusion: the roster cannot be built as written. Something must give - an extra body, a shortened block, or a raised cap - and that decision belongs to the duty officer, not to the clerk drawing the table.
2. The duty NCO proposes posting two certificate holders to the Tower for the whole twelve hours. Evaluate this proposal.
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It is admissible for the Tower but solves nothing else.
The no-consecutive rule means a holder can take at most three Tower blocks (1, 3, 5). Two holders therefore give exactly six Tower blocks: one works 1, 3, 5 and the other 2, 4, 6. The third holder (say C) is then free for the other posts.
But this consumes three blocks from each of two cadets and leaves the harder problem untouched: the binding constraint is B's availability multiplied by the four-block cap, not radio certification. The proposal answers a question nobody asked.
It also has a hidden cost: two of the three certificate holders are now partly committed, leaving less flexibility to cover a Tower absence at short notice. Judgement: accept it as a sub-plan, but present the real choice to the officer - a seventh cadet, or accept one cadet at five blocks.
3. Can the patrol meet the 90-second standard from either the Gate or the Hangar? What would you change?
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Distance coverable in 90 s at 1,4 m/s = 1,4 × 90 = 126 m.
- From the Gate: 250 m → 250 ÷ 1,4 ≈ 179 s - fails by a wide margin.
- From the Hangar: 150 m → 150 ÷ 1,4 ≈ 107 s - still fails, by 17 s.
Neither position satisfies the standing order, and the Hangar only looks acceptable because it is closer.
Options, in order of practicality:
- A static post at the Fuel farm - removes the response-time problem entirely, at the cost of one more body the detachment does not have.
- A vehicle - would need 250 ÷ 90 ≈ 2,8 m/s, plus a driver and fuel.
- Move the patrol to a point within 126 m of the Fuel farm - cheapest, but leaves the Gate uncovered.
Judgement: recommend option 1 and record that the 90-second standard is currently unmet - a standard that is quietly not met is worse than one that is formally reviewed.