Foot Search on a Grid with a Rail Line and a Canal
You are directing a foot-search perimeter after a suspect fled a shoplifting call.
The grid is regular. Avenues run north–south and are numbered 1st through 8th, increasing eastward. Streets run east–west in this order from south to north: Grant, Hayes, Adams, Bell. Every block is the same length.
Two barriers shape the search. A freight rail corridor runs north–south along 6th Avenue, and trains block the crossing; pedestrians can cross 6th Avenue only at Grant and at Adams. A canal runs east–west between Hayes and Adams and can be crossed on foot only at the 4th Avenue bridge.
At 18:02 the suspect is seen at 3rd Avenue and Grant Street and runs east. At 18:05 a witness reports him two blocks north of Grant Street on 4th Avenue, still moving.
Officer Vega is posted at 5th and Adams. Officer Ruiz is at 4th and Hayes. Officer Tran is at 2nd and Bell. A fourth unit is three minutes out.
1. State the suspect's position at 18:05 and explain the trap in the phrase "two blocks north of Grant Street on 4th Avenue."
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Position at 18:05: 4th Avenue and Adams Street.
The trap is that "two blocks north of Grant" invites a fast reader to stop at the first street north and call it Hayes. Count the streets in the stated order: Grant is the southern boundary, Hayes is one block north, Adams is two blocks north. So two blocks north of Grant on 4th Avenue is 4th and Adams, not 4th and Hayes.
Two further points follow from the barriers:
- To get from Grant to Adams on 4th Avenue, the suspect already crossed the canal at the 4th Avenue bridge. He is north of the canal, so the bridge is behind him, not a future obstacle.
- He crossed no rail line, because 6th Avenue is east of 4th. The rail crossing at Adams is still available to him as an eastbound escape route.
Misplacing him one block south at Hayes would put a perimeter on the wrong side of the canal and leave the actual northern exits uncovered.
2. Rank Vega, Ruiz, and Tran by how quickly each can reach 4th and Bell, then recommend where the incoming fourth unit should be posted. Justify with block distances.
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All three are two blocks from 4th and Bell.
- Vega, 5th and Adams: one block west, one block north = 2.
- Ruiz, 4th and Hayes: one block north to Adams, one more to Bell = 2, plus the 4th Avenue bridge.
- Tran, 2nd and Bell: two blocks east along Bell = 2.
The naive answer is "Vega is closest," and it is wrong. Distance does not decide this; containment role does.
Recommendation:
- Ruiz holds the 4th Avenue bridge. He is the only officer south of the canal, and the bridge is the sole foot crossing. He is the backstop if the suspect doubles back, which is worth more than two blocks of pursuit.
- Tran holds Bell Street to the west of 4th, since Bell is the northern boundary and Tran is already on it.
- Vega moves north to 5th and Bell to close the eastern side of that boundary.
- Fourth unit to 6th and Adams - the rail crossing is the one remaining hard exit east, and a unit posted mid-block on 6th Avenue between crossings would be stranded behind the corridor.
With three officers equidistant, assign by chokepoint, not by proximity.
3. If the suspect instead turned east on Adams at 18:06, which intersections could he reach, and which single post would you move first?
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Eastbound on Adams from 4th, he reaches 5th and Adams, then 6th and Adams, where he can cross the rail corridor - the only crossing north of Grant - and continue to 7th and 8th Avenues. From any of those he can turn north to Bell or south toward Hayes, though going south on the east side of 6th leaves him south of the canal with no crossing except by returning to 4th Avenue.
Move Vega first. Vega is already at 5th and Adams, directly on the suspect's path and one block from him; no other officer can be on that line without crossing the grid. Have Vega hold 5th and Adams rather than chase, so the suspect is forced either back west into Tran's boundary or east toward the 6th Avenue crossing.
Only then redirect the fourth unit, which should still take 6th and Adams. The unit's three-minute arrival means it cannot intercept at 5th, but it can be standing on the rail crossing before an eastbound suspect on foot covers two more blocks - provided Vega's position slows him.