A shopping mall has a large basement parking lot with parking slots painted in it along a single row. These slots are quite narrow; a compact car can fit in a single slot but an SUV requires two slots. When a car arrives, the parking attendant guides the car to the first available slot from the beginning of the row into which the car can fit.
For our purpose, cars are numbered according to the order in which they arrive at the lot. For example, the first car to arrive is given a number 1, the second a number 2, and so on. This numbering does not indicate whether a car is a compact or an SUV. The configuration of a parking lot is a sequence of the car numbers in each slot. Each single vacant slot is represented by letter V.
For instance, suppose cars numbered 1 through 5 arrive and park, where cars 1, 3 and 5 are compact cars and 2 and 4 are SUVs. At this point, the parking lot would be described by the sequence 1, 2, 3, 4, 5. If cars 2 and 5 now vacate their slots, the parking lot would now be described as 1, V, V, 3, 4. If a compact car (numbered 6) arrives subsequently followed by an SUV (numbered 7), the parking lot would be described by the sequence 1, 6, V, 3, 4, 7.
Answer the following questions INDEPENDENTLY of each other.
Initially cars numbered 1, 2, 3, and 4 arrive among which 1 and 4 are SUVs while 2 and 3 are compact cars. Car 1 then leaves, followed by the arrivals of car 5 (a compact car) and car 6 (an SUV). Car 4 then leaves. Then car 7 (an SUV) and car 8 (a compact car) arrive. At this moment, which among the following numbered car is parked next to car 3?
Correct Answer :
7
Solution :
The correct answer is 7.
To find which car is parked next to car 3, we need to carefully simulate every arrival and departure, tracking which physical slots each car occupies. Remember: a compact car occupies 1 slot, and an SUV occupies 2 consecutive slots. The attendant always guides a car to the first available slot(s) from the beginning of the row that can fit the car.
Step 1 — Cars 1, 2, 3, and 4 arrive (1 and 4 are SUVs; 2 and 3 are compact cars)
Car 1 (SUV) → needs 2 slots → takes slots 1–2
Car 2 (compact) → needs 1 slot → takes slot 3
Car 3 (compact) → needs 1 slot → takes slot 4
Car 4 (SUV) → needs 2 slots → takes slots 5–6
Parking lot state:
| Slot | 1 | 2 | 3 | 4 | 5 | 6 |
| Car | 1 | 1 | 2 | 3 | 4 | 4 |
Step 2 — Car 1 leaves
Car 1 vacates slots 1 and 2. Both become vacant (V).
| Slot | 1 | 2 | 3 | 4 | 5 | 6 |
| Car | V | V | 2 | 3 | 4 | 4 |
Step 3 — Car 5 (compact) arrives
Car 5 needs 1 slot. The first available single slot from the beginning is slot 1.
| Slot | 1 | 2 | 3 | 4 | 5 | 6 |
| Car | 5 | V | 2 | 3 | 4 | 4 |
Step 4 — Car 6 (SUV) arrives
Car 6 needs 2 consecutive vacant slots. Scanning from the beginning:
- Slot 2 is vacant, but slot 3 is occupied by car 2 → cannot fit here
- Slots 1–6 are all occupied or have only isolated single vacancies
- The first place 2 consecutive vacant slots exist is beyond slot 6, i.e., new slots 7–8 are added at the end.
Car 6 takes slots 7–8.
| Slot | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Car | 5 | V | 2 | 3 | 4 | 4 | 6 | 6 |
Step 5 — Car 4 leaves
Car 4 occupied slots 5 and 6. Both become vacant.
| Slot | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Car | 5 | V | 2 | 3 | V | V | 6 | 6 |
Step 6 — Car 7 (SUV) arrives
Car 7 needs 2 consecutive vacant slots. Scanning from the beginning:
- Slot 2 is vacant, but slot 3 is occupied → only 1 vacant slot here, cannot fit
- Slots 5 and 6 are both vacant → 2 consecutive vacant slots ✓
Car 7 takes slots 5–6.
| Slot | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Car | 5 | V | 2 | 3 | 7 | 7 | 6 | 6 |
Step 7 — Car 8 (compact) arrives
Car 8 needs 1 slot. The first available single vacant slot from the beginning is slot 2.
Car 8 takes slot 2.
| Slot | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Car | 5 | 8 | 2 | 3 | 7 | 7 | 6 | 6 |
Final Analysis — Who is parked next to Car 3?
Car 3 is in slot 4.
- The slot immediately to the left of slot 4 is slot 3 → occupied by Car 2
- The slot immediately to the right of slot 4 is slot 5 → occupied by Car 7
The question asks which of the given options (8, 6, 5, or 7) is parked next to car 3. Car 7 occupies slot 5, which is directly adjacent to slot 4 (where car 3 is parked).
Therefore, the car parked next to car 3 is Car 7.
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