If you read the previous article on this topic, I imagine you were quite annoyed by the nature of its content. The way we use math to find a parking spot in a mall is not something you’d typically hear people talking about at their Christmas parties. However, I think anyone with a modicum of human interest would find this a very curious topic of conversation. The reaction I usually get is one of “Wow. How do you do that?”, or “Can you really use math to find a parking space?”

As I mentioned in the first article, I’ve never settled for getting my math degrees and then doing nothing with it but taking advantage of job opportunities. I wanted to know that this newfound power that I feverishly studied to obtain could be of personal benefit to me: that I could be an effective problem solver, and not only for those highly technical problems but also for more mundane ones like the case at hand. Consequently, I am constantly digging, thinking, and looking for ways to solve everyday problems, or use math to help streamline or streamline an otherwise mundane task. This is exactly how I found the solution to the mall parking spot problem.

Essentially, the solution to this question arises from two complementary mathematical disciplines: Probability and Statistics. In general, one refers to these branches of mathematics as complementary because they are closely related and probability theory needs to be studied and understood before statistical theory can be tackled. These two disciplines help in solving this problem.

Now I am going to give you the method (with some reasoning, fear not, as I will not go into laborious mathematical theory) on how to find a parking space. Give it a try and I’m sure you’ll be amazed (just remember to drop me a line about how great this is). Well, to the method. Understand that we’re talking about finding a spot during rush hour when parking is hard to find; obviously there would be no need for a method under different circumstances. This is especially true during the holiday season (which is actually the time of writing this article, how appropriate).

Ready to try this? let’s go 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 it by the number of cars, which in this example is 180/20 or 9 minutes. Look at the clock and note the time. Within nine minutes from the time you look at your watch, often well before that, one of those twenty or so places will open. The math pretty much guarantees it. Every time I try this and especially when I demonstrate it to someone, I am always amused by the success of the method. While others are feverishly circling the lot, you sit there patiently watching. You choose your territory and simply wait, knowing that in a few minutes the prize is won. What a smug!

So what guarantees you’ll get one of those spots in the allotted time? This is where we start to use a bit of statistical theory. There is a well known theory in Statistics called Central Limit Theory. What this theory essentially says is that, in the long run, many things in life can be predicted by a normal curve. You might remember that this is the bell-shaped curve, with the two tails extending in either direction. This is the most famous 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 are in height, say, relative to the rest of the country. If we are in the 90th percentile for height, then we know that we are taller than 90% of the population. The Central Limit Theorem tells us that eventually all heights, all weights, all IQs in a population eventually smooth out to follow a normal curve pattern. Now what does “eventually” mean? This means that we need a population of things of a certain size for this theorem to apply. The number that works very well is twenty-five, but for the case at hand, twenty will usually suffice. If you can get twenty-five or more cars in front of you, the method works best.

Once we have made some basic assumptions about parked cars, statistics can be applied and we can start making predictions about when parking spaces will be available. We cannot predict which of the twenty cars will go first, but we can predict that one of them will do so within a given time period. This process is similar to the one used by a life insurance company when it is able to predict how many people of a certain age will die in the following year, but not which ones will die. To make such predictions, the company relies on so-called life tables, and these are based on probability and statistical theory. In our particular problem, we assume that in three hours all twenty cars will have rolled over and will be replaced by another twenty cars. To reach this conclusion, we have used some basic assumptions about two parameters of the Normal Distribution, the mean and the standard deviation. For the purposes of this article I will not go into detail about these parameters; the main goal is to show that this method will work very well and can be tried next time.

In short, pick your spot 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 accurate information.) ). Once you’ve set your time slot, you can check your clock and make sure a spot will be available in a maximum of 9 minutes, or whatever time slot you’ve calculated based on the number of cars you’re working with; and that due to the nature of the Normal curve, a spot will often become available before the maximum allotted time. Try this and you will be surprised. At a minimum, you’ll score points with friends and family for your intuitive nature.