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Mathematicians don’t exactly have a reputation as being a party crowd, staying up till all hours drinking at the bars. One group of them, however, seems to have set out to prove that math lovers can enjoy a good pub crawl as much as anyone. In fact, they are willing to put in the work needed to do the most efficient pub crawl of all.
What does that mean exactly? Well, there is a math puzzle known as the salesman problem. The puzzle requires you to find out the quickest way of visiting every point on a given map once, and only once, and then return back to the original point. In the classic example of this, a map would be written out with say 5 locations on it and the distances between them. The person solving the problem needs to determine the quickest way to get to them all in order to be correct.
This is a very popular math problem precisely because the answer is typically not what one would guess at first glance. Instead, the solver needs to calculate out how to hit the points efficiently, even if it isn’t intuitive.
What does that have to do with mathematicians and drinking? Well, a group of mathematicians solved a particularly complicated version of the salesman problem. They mapped out the most efficient way to engage in a pub crawl where someone visits every single one of the bars in South Korea. That is 81,998 bars in total.
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In a write-up about the accomplishment, William Cook, who is a professor of combinatorics and optimization at the University of Waterloo in Canada and one of the members of the team who solved this particular problem, said:
“It would be a very long pub crawl. The total walking time for the round trip is 15,386,177 seconds, or 178 days, 1 hour, 56 minutes, and 17 seconds. You will need to stop for plenty of drinks along the way.”
This is definitely a fun and interesting version of the math problem, but why is it noteworthy? Well, solving this type of problem gets MUCH harder as you add in more points on the map. While solving a salesmen problem with just 5-6 points is relatively easy, solving one with over 80,000 is no simple task at all. To give an idea of how complicated this problem really is, it helps to look at just how many potential paths (and there for solutions) to this problem there are.
If one tried to solve this salesmen problem using just brute force (guessing every possible path) they would have to guess for a very long time. The number of potential solutions is a 2 followed by about 367,308 zeros. If you had a computer guessing one million different path combinations per second, it would take longer than the universe has been in existence.
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This is what makes the problem so important. It requires the mathematicians work to come up with the most efficient ways of solving problems with extraordinarily large sets of data. Having this ability can then be applied to other areas of life, as Cook explains:
“We use large examples of the traveling salesman problem as a means for developing and testing general-purpose optimization methods. The world has limited resources and the aim of the applied mathematics fields of mathematical optimization and operations research is to create tools to help us to use these resources as efficiently as possible.”
So yes, finding the best way to go on a pub crawl with almost 82,000 bars is actually helpful for humanity.
It is not, however, recommended for anyone to actually do if they care about their liver.
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