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## Finding a Mall Parking Spot Using Mathematics – Part II

If you have read the previous article on this topic, then I imagine you were quite stung by the nature of its content. The way we use math to find a parking spot in a mall is not a typical thing people discuss at their Christmas parties. Still, I think anyone with a modicum of human interest would find this topic of conversation most intriguing. The reaction I usually get is “Wow. How do you do that?” or “Can you really use math to find a parking spot?”

As I mentioned in the first post, I never just got my math degrees and did nothing with them but take advantage of job opportunities. I wanted to know that this newly discovered power that I was feverishly studying to obtain could actually benefit my personal benefit: that I would be able to solve problems effectively, and not just for these highly technical problems, but also for more mundane problems. such as in the present case. Therefore, I constantly probe, ponder, and search for ways to solve everyday problems or use math to help optimize or streamline an otherwise mundane task. This is exactly how I came across the solution to the mall parking problem.

Essentially, the solution to this question stems from two complementary mathematical disciplines: probability and statistics. Generally, these branches of mathematics are called complementary because they are closely related and it is necessary to study and understand the theory of probability before being able to tackle statistical theory. These two disciplines help solve this problem.

Now I’m going to give you the method (with a bit of reasoning – never fear, because I won’t go into laborious mathematical theory) on how to find a parking space. Try this and I’m sure you’ll be amazed (don’t forget to tell me how cool it is). Okay, to the method. Understand that we’re talking about finding a spot during peak hours when parking is hard to come by – obviously there wouldn’t be a need for a method in different circumstances. This is especially true during the Christmas season (which is actually when this article is written – how apropos).

Ready to try this? Let’s go. The next time you go to the mall, choose a waiting area that allows you to see a total of at least twenty cars in front of you on each side. The reason for the number twenty will be explained later. Now take three hours (180 minutes) and divide that by the number of cars, which in this example is 180/20 or 9 minutes. Take a look at the clock and observe the time. Within nine minutes of looking at the clock – often quite early – one of these twenty spots will open. The math pretty much guarantees it. Every time I test this and especially when I demonstrate it to someone, I am always amused by the success of the method. While others feverishly circle the pitch, you sit there patiently watching. You choose your territory and wait, knowing that within minutes the prize is won. How smug!

So what guarantees that you will get one of these places in the given time. This is where we start using a bit of statistical theory. There is a well-known theory in statistics called the central limit theory. What this theory basically says is that over the long term, many things in life can be predicted by a normal curve. This, you may recall, is the bell-shaped curve, with the two tails extending in either direction. This is the best known statistical curve. For those of you wondering, a statistical curve is a graph from which we can read information. Such a graph allows us to make educated guesses or predictions about populations, in this case the population of cars parked at the local mall.

Graphs like the normal curve tell us where we stand in height, say, relative to the rest of the country. If we are in the 90th percentile for height, then we know we are taller than 90% of the population. The central limit theorem tells us that eventually all heights, all weights, all intelligence quotients in a population eventually smooth out to follow a normal curve pattern. Now what does “eventually” mean. This means that we need a certain population size of objects for this theorem to apply. The number that works very well is twenty-five, but for our case, twenty will usually suffice. If you can have twenty-five or more cars in front of you, the better the method works.

Once we’ve made some basic assumptions about parked cars, the statistics can be applied and we can start making predictions about when parking spots might become available. We can’t predict which of the twenty cars will leave first, but we can predict that one of them will leave within a certain amount of time. This process is similar to that used by a life insurance company when it is able to predict how many people of a certain age will die the following year, but not which ones will die. To make such predictions, the company relies on so-called mortality tables, and these are based on probability and statistical theory. In our particular problem, we assume that within three hours all twenty cars will have turned around and been replaced by twenty other cars. To reach this conclusion, we made some basic assumptions about two parameters of the normal distribution, the mean and the standard deviation. For the purposes of this article, I won’t go into detail about these settings; the main goal is to show that this method will work very well and can be tested next time.

To summarize, choose your place in front of at least twenty cars. Divide 180 minutes by the number of cars – in this case 20 – to get 9 minutes (Note: for twenty-five cars the time interval will be 7.2 minutes or 7 minutes and 12 seconds, if you really want to be precise ). Once you have established your time interval, you can check your watch and be sure that a space will be available in a maximum of 9 minutes, or whatever interval you have calculated depending on the number of cars with which you work ; and that due to the nature of the normal curve, a place will often become available sooner than the maximum time allowed. Try this and you will be surprised. At the very least, you’ll score points with your friends and family for your intuitive nature.

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