Instructions

A shopping mall has a large basement parking lot with parking slots painted in it along aĀ single row. These slots are quite narrow; a compact car can fit in a single slot but an SUVĀ requires two slots. When a car arrives, the parking attendant guides the car to the firstĀ 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. ForĀ example, the first car to arrive is given a number 1, the second a number 2, and so on. ThisĀ numbering does not indicate whether a car is a compact or an SUV. The configuration of aĀ parking lot is a sequence of the car numbers in each slot. Each single vacant slot isĀ represented by letter V.

For instance, suppose cars numbered 1 through 5 arrive and park, where cars 1, 3 and 5 areĀ compact cars and 2 and 4 are SUVs. At this point, the parking lot would be described by theĀ sequence 1, 2, 3, 4, 5. If cars 2 and 5 now vacate their slots, the parking lot would now beĀ described as 1, V, V, 3, 4. If a compact car (numbered 6) arrives subsequently followed by anĀ 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.

Question 22

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

Solution

Let's look at option 4.

Order of cars is 8,2,3,V,5,6,7. This sequence is easily possible.

Let's say cars 1,2,3,4,5,6,7 arrive one after the another.

Now Car 1 leaves and Car 8 takes that place.

Finally Car 4 leaves. Hence we can see that this combination of cars is possible

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