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.

Suppose eight cars have arrived, of which two have left. Also suppose that car 4 is a compact and car 7 is an SUV. Which of the following is a POSSIBLE current configuration of the parking lot?

The correct option is 8, 2, 3, V, 5, 6, 7.

To understand why this is a possible current configuration of the parking lot, we can trace the arrival, parking, and departure of the cars step-by-step. Since eight cars arrived in total (numbered 1 through 8) and exactly two have left, the configuration must contain six of the original cars and some vacant slots (represented by V). In the correct option, the present cars are 8, 2, 3, 5, 6, and 7, which means the two cars that left are 1 and 4.

Let us define the sizes of the cars based on the given constraints and a valid scenario:
- Car 4 is a compact car (requires 1 slot).
- Car 7 is an SUV (requires 2 slots).
- Let Cars 1, 3, 5, 6, and 8 be compact cars (each requiring 1 slot).
- Let Car 2 be an SUV (requiring 2 slots).

We can now trace the chronological sequence of events:

1. Arrival of Cars 1, 2, 3, and 4:
- Car 1 (compact) arrives and parks in slot 1.
- Car 2 (SUV) arrives and occupies the first available space large enough, which is slots 2 and 3.
- Car 3 (compact) arrives and parks in the next available slot, slot 4.
- Car 4 (compact) arrives and parks in slot 5.
At this point, the slots look like:
Slot 1: Car 1 | Slots 2–3: Car 2 | Slot 4: Car 3 | Slot 5: Car 4

2. Arrival of Car 5:
- Car 5 (compact) arrives. The first available slot is slot 6 (since slots 1 to 5 are occupied).
Slot 1: Car 1 | Slots 2–3: Car 2 | Slot 4: Car 3 | Slot 5: Car 4 | Slot 6: Car 5

3. Arrival of Car 6:
- Car 6 (compact) arrives and parks in the next available slot, slot 7.
Slot 1: Car 1 | Slots 2–3: Car 2 | Slot 4: Car 3 | Slot 5: Car 4 | Slot 6: Car 5 | Slot 7: Car 6

4. Arrival of Car 7:
- Car 7 (SUV) arrives and occupies the first available pair of adjacent slots, which are slots 8 and 9.
Slot 1: Car 1 | Slots 2–3: Car 2 | Slot 4: Car 3 | Slot 5: Car 4 | Slot 6: Car 5 | Slot 7: Car 6 | Slots 8–9: Car 7

5. Departure of Cars 1 and 4:
- Cars 1 (slot 1) and 4 (slot 5) vacate their positions, leaving those slots empty (V).
Slot 1: V | Slots 2–3: Car 2 | Slot 4: Car 3 | Slot 5: V | Slot 6: Car 5 | Slot 7: Car 6 | Slots 8–9: Car 7

6. Arrival of Car 8:
- Car 8 (compact) arrives. The first available slot from the beginning of the row is slot 1, so it parks in slot 1.
Slot 1: Car 8 | Slots 2–3: Car 2 | Slot 4: Car 3 | Slot 5: V | Slot 6: Car 5 | Slot 7: Car 6 | Slots 8–9: Car 7

Representing this final layout as a sequence (where each compact car or vacant slot takes up one position, and each SUV takes up one position representing its occupied block), we obtain:
8, 2, 3, V, 5, 6, 7

This matches the correct configuration perfectly, confirming that it is a possible state of the parking lot.