168 views

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 $\text{SUV}$ 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 $\text{SUV}$. 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 $\text{SUV}$s. 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 $1, \text{V, V,}3,4.$ If a compact car (numbered $6$) arrives subsequently followed by an $\text{SUV}$ (numbered $6$), arrives subsequently followed by an $\text{SUV}$ (numbered 7), the parking lot would be described by the sequence $1,6, \text{V},3,4,7.$

Initially cars numbered $1,2,3$ and $4$ arrive among which $1$ and $4$ are $\text{SUV}$s 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 $\text{SUV)}$ and car $8$ (a compact car) arrive. At this moment, which among the following numbered car is parked next to car $3?$

1. $8$
2. $6$
3. $5$
4. $7$