पिकेट से संदिग्ध के मार्ग की गणना और दुकानों का क्रम
You are posted at a picket at the main gate of a colony, point P. At 9:10 pm an informer describes a suspect's movement: he started from P, walked 400 m north, turned right and walked 300 m, turned right again and walked 200 m, then turned left and walked 250 m, and entered a lane at point T. A patrol jeep is standing at P. It can use only the straight colony roads that run north-south and east-west; there are no diagonal shortcuts and no cuts through plots. Separately, four shops on one straight road were burgled on four consecutive nights: a chemist, a bakery, a tailor and a grocery. From west to east, the case diary fixes only this: the bakery is not at either end of the row; the tailor is immediately east of the bakery; the chemist is somewhere west of the tailor; the grocery is east of the bakery. The informer adds one more line: 'He turned right only twice, so he must have ended up south of the gate.'
1. Locate point T relative to P and calculate the shortest road distance the jeep must cover. Show each step.
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Take P as (0, 0), north as +y and east as +x.
Step 1: 400 m north: (0, 400). Facing north. Step 2: right turn from north means east, 300 m: (300, 400). Facing east. Step 3: right turn from east means south, 200 m: (300, 200). Facing south. Step 4: left turn from south means east, 250 m: (550, 200). That is T.
So T is 550 m east and 200 m north of P, that is, north-east of the picket.
Road distance on the grid must be measured along the roads, so it is 550 + 200 = 750 m. The straight-line distance would be the square root of (550 squared + 200 squared), about 585 m, but the jeep cannot use it.
The turn count matters, the direction faced matters, and the north-south and east-west legs must be added separately. Mixing the legs is the usual error.
2. Fix the west-to-east order of the four shops. Which shop was immediately east of the bakery, and which shop stood at the western end?
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Number the positions 1 to 4 from west to east.
Clue 1: the bakery is not at either end, so it is at 2 or 3. Clue 2: the tailor is immediately east of the bakery. If the bakery were at 3, the tailor would be at 4, leaving no position east of the bakery for the grocery. Therefore the bakery is at 2 and the tailor at 3. Clue 3: the grocery is east of the bakery, and position 4 is the only free place east of the bakery, since 3 is the tailor. Grocery at 4. Clue 4: the chemist is west of the tailor. The only free position west of 3 is 1.
Order west to east: chemist, bakery, tailor, grocery.
The shop immediately east of the bakery is the tailor, and the western end was the chemist. Checking the order against all four clues at the end is the safeguard against a forced arrangement.
3. Evaluate the informer's claim that because the suspect turned right twice, he must be south of P.
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The claim is false. Turning right twice changes the direction faced, not the net position. After the first right the suspect faced east; after the second right he faced south. Facing south at the end of the walk says nothing about where he is relative to P.
Compute the net displacement: north-south = 400 m north minus 200 m south = 200 m north. East-west = 300 m east plus 250 m east = 550 m east. The suspect is 200 m north of P, not south.
The general rule: count displacement along each axis, with direction signs. The number of turns is irrelevant to position; only the length and direction of each leg matter. A constable should record the legs, not the turns, because the turns are what mislead. The same discipline applies when checking a witness's route statement.