Four beats, four modes: solving the deployment grid and then breaking it
You are preparing the night deployment order for a four-constable patrol in a market area with four beats: Bus Stand, Hospital Road, Old Market and Canal Bridge. Each constable takes exactly one beat and uses exactly one mode of movement - Bolero, motorcycle, bicycle or on foot - and no two share a beat or a mode. The station notes give five facts. (i) Gita is assigned to Hospital Road. (ii) Farooq uses the motorcycle and is not at the Bus Stand. (iii) The officer at Canal Bridge uses the Bolero. (iv) Imran is at the Bus Stand and moves on foot. (v) Harpreet does not use the bicycle. Crime data for the last 30 days show that 6 of the 10 snatchings reported in the area took place within 300 m of the Bus Stand, all between 8 pm and 10 pm, and that the lane behind the vegetable market can be reached only on foot. Farooq's brother-in-law runs a scrap shop 40 m from the Canal Bridge, and that scrap dealer is named in an unrelated theft case pending at the station.
1. Solve the grid completely. State each deduction in order.
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Deduction chain:
- From (i), Gita = Hospital Road; from (iv), Imran = Bus Stand, on foot.
- Only Old Market and Canal Bridge remain for Farooq and Harpreet.
- From (iii), Canal Bridge = Bolero. From (ii), Farooq = motorcycle. A constable uses only one mode, so Farooq cannot be the Canal Bridge officer. Therefore Farooq = Old Market, motorcycle and Harpreet = Canal Bridge, Bolero.
- The only unused mode is the bicycle and the only unassigned officer is Gita, so Gita = Hospital Road, bicycle. Fact (v) is satisfied because Harpreet has the Bolero, not the bicycle.
Why the solution is unique: step 3 is forced by the mode conflict, and once Farooq and Harpreet are placed, the last mode is forced. No alternative assignment survives the clues.
Final grid: Gita - Hospital Road - bicycle; Farooq - Old Market - motorcycle; Harpreet - Canal Bridge - Bolero; Imran - Bus Stand - on foot.
2. Using the grid and the crime data, is this a sound deployment for 8 pm to 10 pm? If not, what would you change?
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It is not sound. The grid is logically correct but tactically wrong.
- The Bus Stand carries 60% of the snatchings (6 of 10) and is the only beat with a constable on foot. Foot patrol is excellent for the lane behind the vegetable market, but a chain-snatching accused on a motorcycle will outrun a constable on foot the moment he regains the main road.
- The motorcycle is with Farooq at Old Market, a beat with no reported snatchings in the sample.
Recommended change, with reasons recorded in the order:
- Move the motorcycle to the Bus Stand beat for 8 pm–10 pm, and give Old Market the bicycle. The grid clue set is a starting point; a deployment order may be varied by the SHO for operational reasons if the variation is written down.
- Pair the Bus Stand officer with a Home Guard on foot who covers the lane behind the market, so both the pursuit and the lane are covered.
- Note that the hotspot window is exactly 8–10 pm - do not spread the motorcycle across the whole shift; place it at the stand for those two hours and let it patrol the connecting roads afterwards.
- Keep the Canal Bridge officer on the Bolero for highway response, but brief him that he is not to touch the scrap-dealer case.
3. How do you handle the relationship between Farooq and the scrap dealer named in the pending theft case?
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A conflict of interest exists, but it is currently latent, not actual. After the grid, Farooq is at Old Market, not Canal Bridge, so he is not deployed at his relative's location. That reduces the risk but does not remove it.
Actions:
- Record the relationship in writing in the station diary and in the case file of the scrap-dealer theft, so that the disclosure exists before anything is recovered from that shop.
- Keep Farooq out of every step of that case - no search of the scrap shop, no seizure, no recording of the dealer's statement, no verification of the scrap register. Assign an officer from another beat.
- Brief the Canal Bridge officer that if any recovery or enquiry touches the scrap shop, he reports to you and not to Farooq.
- If Farooq is unexpectedly drawn into the case, he must disclose immediately and withdraw; a failure to disclose is a disciplinary matter.
- In the deployment order, do not write the reason as a stigma - record it as a standard conflict-of-interest recusal, which protects both the officer and the prosecution.