Three Cars, Three Jobs
At the morning briefing a sergeant sketches a logic problem on the whiteboard. Three patrol cars - Alpha, Bravo and Charlie - each attended exactly one of three jobs: a theft, a vandalism and a collision. Each job occurred in a different suburb: Ashgrove, Bellview or Crayford. Five clues are given and nothing else is said. (1) Alpha did not attend Ashgrove. (2) The collision was in Crayford. (3) Bravo attended the theft. (4) Charlie did not attend Bellview. (5) The vandalism was in Bellview. A constable objects that there is not enough information to solve it.
1. Assign each car to a job and a suburb, showing the deduction step by step.
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Step 1. Clue 2 fixes collision = Crayford. Clue 5 fixes vandalism = Bellview.
Step 2. Three suburbs, three jobs, one each - so theft = Ashgrove (the only suburb left). Clue 3 puts Bravo on the theft, so Bravo = theft = Ashgrove.
Step 3. Alpha and Charlie now split collision/Crayford and vandalism/Bellview.
Step 4. Clue 4 says Charlie was not at Bellview. Vandalism is the Bellview job, so Charlie cannot be the vandalism car. Therefore Charlie = collision = Crayford and Alpha = vandalism = Bellview.
Step 5. Check clue 1: Alpha is at Bellview, which is not Ashgrove. Satisfied.
| Car | Job | Suburb |
|---|---|---|
| Alpha | Vandalism | Bellview |
| Bravo | Theft | Ashgrove |
| Charlie | Collision | Crayford |
Why the constable is wrong: the solution is forced, not guessed. Each step eliminates possibilities rather than assuming one; the check in Step 5 is what distinguishes a deduction from a plausible guess.
2. One of the five clues adds nothing, and one cannot be removed. Identify both and prove your answer.
Read the worked answer
The redundant clue is (1), 'Alpha did not attend Ashgrove'. Once clue 5 makes Bellview the vandalism suburb and clue 2 makes Crayford the collision suburb, Ashgrove can only be the theft suburb. Clue 3 gives the theft to Bravo, and each job has exactly one car, so Alpha can never be the theft car and therefore can never be at Ashgrove. Clue 1 is true, but it is entailed - deleting it changes no assignment.
A clue that cannot be removed is (3), 'Bravo attended the theft'. Delete it and a second assignment survives every remaining clue:
| Car | Job | Suburb |
|---|---|---|
| Alpha | Collision | Crayford |
| Bravo | Vandalism | Bellview |
| Charlie | Theft | Ashgrove |
Check against (1) Alpha not Ashgrove: true. (2) Collision at Crayford: true. (4) Charlie not Bellview: true. (5) Vandalism at Bellview: true. So without clue 3 the puzzle has two solutions and the sergeant's claim of sufficiency collapses.
Same test on clue (4): delete it and Alpha = collision/Crayford, Charlie = vandalism/Bellview, Bravo = theft/Ashgrove also satisfies the rest. Clue 4 is therefore also load-bearing.
Method: a clue is redundant if the other clues already entail it; a clue is necessary if deleting it admits at least one extra consistent assignment.