The Smudged Naka Register on NH-33
Five vehicles were intercepted at the excise naka on NH-33 near Ormanjhi on a Saturday night, one every 35 minutes from 19:10 to 21:30. Each carried a different number of 750 ml bottles - 24, 48, 60, 72 and 96 - and each had come from a different district: Dhanbad, Hazaribagh, Bokaro, Ramgarh and Ranchi. The five vehicle types involved were truck, Bolero, Scorpio, Summoner and auto-rickshaw. Rain has smudged the register, and only these entries survive: (i) the truck was stopped first; (ii) the last vehicle, an auto-rickshaw, carried 60 bottles; (iii) the vehicle from Ramgarh carried 72 bottles and was stopped immediately after the Bolero, which carried 96 bottles; (iv) the Scorpio carried 24 bottles and was stopped exactly two places before the Ramgarh vehicle; (v) the vehicle carrying 48 bottles came from Dhanbad; (vi) the vehicle from Bokaro was stopped immediately after the vehicle from Hazaribagh. The inspector must decide which vehicles to send for detailed investigation.
1. Reconstruct the register completely: position, time, vehicle type, bottles and district of origin for all five interceptions. Show the deduction step by step.
Read the worked answer
Fixed points from (i) and (ii)
- Position 1 = truck; position 5 = auto-rickshaw with 60 bottles.
Placing the Bolero–Ramgarh pair, 96 then 72
- The pair must occupy consecutive positions: (1,2), (2,3), (3,4) or (4,5).
- Position 1 is the truck, so (1,2) fails. Position 5 is the auto-rickshaw with 60 bottles, so (4,5) fails.
- The pair is therefore (2,3) or (3,4).
Placing the Scorpio, two places before Ramgarh
- If Ramgarh were at position 3, the Scorpio would be at position 1 - impossible, that is the truck.
- So Ramgarh is position 4, the Scorpio is position 2, and the Bolero (96 bottles) is position 3.
Filling the remaining slots
- Position 4 = Summoner (only type left), 72 bottles, Ramgarh
- Position 1 = truck, 48 bottles (only count left), from Dhanbad by (v)
Districts
- Bokaro comes immediately after Hazaribagh. Position 1 is already Dhanbad and position 4 is Ramgarh, so the only free consecutive pair is (2,3): position 2 = Hazaribagh, position 3 = Bokaro, leaving position 5 = Ranchi.
Result
| Pos | Time | Vehicle | Bottles | From |
|---|---|---|---|---|
| 1 | 19:10 | Truck | 48 | Dhanbad |
| 2 | 19:45 | Scorpio | 24 | Hazaribagh |
| 3 | 20:20 | Bolero | 96 | Bokaro |
| 4 | 20:55 | Summoner | 72 | Ramgarh |
| 5 | 21:30 | Auto-rickshaw | 60 | Ranchi |
| Every clue is used exactly once, and no alternative assignment survives the test. |
2. How many bottles and how many litres were seized in all, and what percentage of the total does the largest single seizure represent?
Read the worked answer
Bottles
- 48 + 24 + 96 + 72 + 60 = 300 bottles
Volume
- 300 × 0.75 L = 225 litres
Largest seizure
- Bolero, 96 bottles
- 96 ÷ 300 × 100 = 32%
Useful cross-check
- The average load is 300 ÷ 5 = 60 bottles per vehicle. The Bolero is therefore 1.6 times the average, while the Scorpio is only 0.4 times it. Expressing the figures against the average is a quick way to describe the spread in the case diary without implying that the average load is itself lawful.
3. The inspector decides to send for detailed investigation only those vehicles whose load exceeded the average load of the five. Which vehicles qualify, and is that a sound decision rule?
Read the worked answer
Applying the rule
- Average load = 60 bottles
- Loads above 60: Bolero (96) and Summoner (72)
- Together they hold 168 bottles, i.e. 56% of the total from two of the five vehicles
Is it sound?
- As a first filter it works: it concentrates effort where the bulk of the offending quantity is, and 168 bottles justify a full investigation on volume grounds alone.
- As a complete rule it is weak. The Scorpio carried only 24 bottles, yet a small load in a private vehicle often indicates a courier moving a consignment in instalments rather than a trader moving stock; volume alone would let such a runner go.
- The auto-rickshaw with exactly 60 bottles fails the test only by definition - it sits on the average, not above it.
- The quantities also vary independently of vehicle type and origin, so quantity cannot stand in for other risk factors.
Better rule Send for investigation any vehicle that is either above the average load or lacks a satisfactory transport document or whose stated origin does not match the route. In this puzzle the data give quantity, type and origin as separate facts precisely because a constable is expected to weigh all three, not just the biggest number.