If you read the previous article on this topic, I imagine the nature of its content stung you quite a bit. The way we use math to find a place to park in a mall is not typical of what you hear people talking about at their Christmas parties. However, I think anyone with a modicum of human interest will find this topic of conversation very curious. The reaction I usually get is “Wow. How do you do it?”, Or “Can you really use math to find a place to park?”

As I mentioned in the first article, I was never content with getting my math degrees and then doing nothing with them other than taking advantage of job opportunities. I wanted to know that this newfound power that I feverishly studied to obtain could actually redound to my personal benefit – that it could be an effective problem solver, and not just for those highly technical problems, but also more mundane ones like the case that occupies us. Consequently, I am constantly researching, thinking, and looking for ways to solve everyday problems, or using mathematics to help optimize or simplify an otherwise mundane task. This is exactly how I found the solution to the mall parking problem.

Essentially, the solution to this question arises from two complementary mathematical disciplines: probability and statistics. Generally, one refers to these branches of mathematics as complementary because they are closely related and probability theory needs to be studied and understood before attempting to tackle statistical theory. These two disciplines help solve this problem.

Now I am going to give you the method (with some reasoning, fear not, as I will not go into a laborious mathematical theory) on how to find a place to park. Give this a try and I’m sure you will be surprised (just remember to write to me about how cool this is). Well, to the method. Please understand that we are talking about finding a spot during peak hours when parking is difficult; obviously, there would be no need for a method in 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. 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 it by the number of cars, which in this example is 180/20 or 9 minutes. Take a look at the clock and note the time. In a nine-minute interval from when you look at the clock, often well before, one of those twenty or more points will open. Mathematics practically guarantees this. Whenever I try this and especially when I demonstrate it to someone, I am always amused by the success of the method. As others spin feverishly through the parking lot, you sit there patiently watching. You choose your territory and you just wait, knowing that in a few minutes the prize will be won. How conceited!

So what guarantees that you will get one of those spots in the allotted time? This is where we start to use a little statistical theory. There is a well-known theory in statistics called the 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. This, as you may recall, 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. This 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, with respect 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 intelligence quotients of 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 things for this theorem to apply. The number that works very well is twenty-five, but for our present case, twenty will be enough. If you can put twenty-five or more cars in front of you, the method will work better.

Once we’ve made some basic assumptions about parked cars, statistics can be applied and we can begin to make predictions about when parking spots will be available. We cannot predict which of the twenty cars will go out first, but we can predict that one of them will go out within a certain period of time. This process is similar to what a life insurance company uses when it can 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 mortality tables, and these are based on probability theory and statistics. In our particular problem, we assume that within three hours all twenty cars will have tipped 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, 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’ve set your time slot, you can check your watch and make sure a spot will be available in a maximum of 9 minutes, or whatever slot you’ve calculated depending on the number of cars you’re working with; and that due to the nature of the Normal curve, a spot will be available before the maximum time allotted. Try this and you will be amazed. At the very least, you’ll score points with friends and family for your intuitive nature.