Four Stands, Four Cadets
Four officer cadets - A, B, C and D - must each be assigned to exactly one training stand: bridge, radio, first aid or map. The following rules apply.
- A is not qualified for radio or first aid.
- B must be assigned to either bridge or map.
- If D is assigned to map, then C must be assigned to radio.
- D cannot be assigned to first aid.
- A has not qualified on map.
Each stand runs three 20-minute rotations beginning at 09:00. Attendance is recorded at the start of each rotation. A visiting instructor will inspect at 10:05, after the rotations have ended. The cadets must also be available for a briefing at 10:10. One cadet has a medical appointment at 10:30 and must be released by 10:20.
1. Determine the unique assignment of cadets to stands. Show your deduction step by step.
Read the worked answer
From rule 1, A is neither radio nor first aid. Rule 5 removes map, so A must be bridge. Rule 2 says B is bridge or map; bridge is already taken by A, so B must be map. The remaining stands are radio and first aid, and the remaining cadets are C and D. Rule 4 says D cannot be first aid, so D must be radio and C must be first aid. Check rule 3: 'If D is map, then C is radio.' D is not map, so the condition is not triggered and the rule is satisfied. The assignment is A - bridge, B - map, C - first aid, D - radio. The key move is to use rule 5 with rule 1 to fix A before trying the conditional rule 3. Candidates who start with rule 3 often assume D is on map, which is not stated.
2. If B and C swap stands, which rule is broken and which rules remain satisfied?
Read the worked answer
After the swap, B is on first aid and C is on map. Rule 2 is broken: B must be on bridge or map, and B is now on neither. Rule 1 remains satisfied because A is still on bridge. Rule 4 remains satisfied because D is still on radio, not first aid. Rule 5 remains satisfied because A is not on map. Rule 3 is not triggered because D is not on map; if anything, the swap makes rule 3 irrelevant rather than broken. The answer should distinguish a broken rule from a rule whose condition is false. A conditional rule such as rule 3 is not violated merely because its 'if' part does not occur. This distinction is the point of the question: the swap fails for a direct assignment rule, not for the conditional one.
3. How many complete rotations occur before the 10:05 inspection, and what is the latest time the cadet with the 10:30 appointment can leave the stand area without missing a rotation?
Read the worked answer
Each rotation is 20 minutes. Rotation 1 runs 09:00–09:20, rotation 2 runs 09:20–09:40, and rotation 3 runs 09:40–10:00. The inspection is at 10:05, so three complete rotations have finished, and the cadets are free from 10:00 until the 10:10 briefing. The cadet with the 10:30 appointment must be released by 10:20. The briefing starts at 10:10; if it lasts the usual 10 minutes, it ends at 10:20, which leaves no travel margin. The safe planning answer is to release that cadet from the briefing by 10:15 and confirm travel time to the medical facility. The candidate should not simply say 'after the third rotation' because the briefing and travel margin are part of the constraint. Stating a latest departure time of 10:20 ignores walking time and queues and is therefore too tight.