Parking Sequences

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Grade Vs Difficulty:
  EasyModerateChallengingPerplexing
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13-14
 

We are going to take a look at a problem that deals with parking cars in a one-way
parking lot. Each driver in a line of cars will choose which parking spot they prefer to park in. The list of preferred parking spots is called a parking sequence. When they come to their desired parking spot, if it is open they can park there, if it is not open, they will park in the next open spot. Not all parking sequences result in all cars ending in a parking spot. There are many arrangements that do result in all cars in a parking spot. We will work to find how many of these sequences exist.