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Daniel Kluver

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Skittles math

For this blog I am going to do something a little different. I was at a play when one of my friends made an offhand remark: "If you take all the skittles in the world and lie them in a line you can wrap them around the world" I found this pretty hard to believe, so while waiting for the play to start I decided to figure out the truth.

As it goes, the math behind this isn't too difficult. The first question we want to know is how many skittles would it take to wrap around the world. For the size of an average skittle I had to turn to yahoo answers, where I got the number 1.5cm. As far as information sources go yahoo answers isn't a great source, particularly since some answers weren't sure if we were talking about candy or a British game, that said 1.5cm sounds about right, and is probably accurate enough for our purposes. The diameter of the earth is 14,742km. Putting these together, we would need 849,466,667 skittles.

This is a lot of skittles, the average 2oz bag of skittles of skittles only has 54 skittles so we are talking about almost sixteen million bags of skittles (15,730,864). Ordered on Amazon this could cost almost 10 million dollars, although I'm sure at that scale you could get a discount from the manufacturer. Whether or not this little adventure would be cheap, however, isn't really our concern. The question is whether that many skittles exist. To answer that question we turn to wrigley.com the website of the manufacturer of skittles, who claim to make over 200 million skittles a day. This means that one weeks worth of skittles production is enough to wrap around the world. I find it pretty believable that the line from skittle production to consumer stomach takes at least a week on average (who knows how long the average bag of skittles lasts on a store shelf), so I feel like it would be reasonable to conclude that, yes, all of the skittles could wrap around the world at least once.

How did the skittles get there?

Having answered "are there enough skittles", now I want to ask a different question: "How did the skittles get there?" Skittles don't just decide to be in a solid ring around the world, and skittles don't float. Is it possible for someone to place skittles in a row fast enough for the skittles not to sink before the skittle ring is completed? For any small number of normal people the answer is no: gravity acts pretty fast, and the world is pretty big. By the time any normal person could go around the world any skittles placed over water will not be where they started. There are enough people in the world that we could theoretically first get a ring of people and then on some mark (probably sent by satellite) the 850 million people could each place their candy, but that plan is silly.

So could any one person hope to make a skittle ring around the world. What about The Flash? The Flash is a superhero by DC comics endowed with super speed. Could The Flash make the trip around the world fast enough to still have a mostly coherent line of skittles?

To get an answer to this we need to know how fast The Flash is. This is where we run into a problem, as it turns out different comics pace The Flash at pretty different speeds. Lets be generous; lets assume that The Flash moves at the speed of light. In this case he could run across the entire earth seven times in one second. In the time it takes The Flash to run around the world once the skittle would fall almost 8 centimeters. While this is taller than a skittle, its not so tall The Flash couldn't account for it, even if he gets it wrong the first time he can always do it again. Even if it takes him seven tries to get right the whole experiment still finishes under a second.

Unfortunately for The Flash, these calculations assume that The Flash can carry 850 million skittles. The average skittle weights about one gram, meaning that the 850 million skittles would weigh about 850 metric tons (almost two million pounds) The Flash is by no means weak, and is probably at or slightly above the peak human fitness in terms of lifting and carrying, being able to carry two or three people at once when evacuating a danger zone, but he also isn't Superman, and therefore cannot lift that much candy. If we assume that the flash can lift about 240kg (roughly 3 adult humans) he would have to take 3,500 trips. Even if all this backtracking only slows the flash down by a factor of one hundred that would make the 8 centimeter fall an 8 meter fall, which is probably too large for the flash to account for (without further slowdown)

Lets talk Superman for a second. Superman is strong enough to lift the candy. If we assume that Superman is only as fast as a speeding bullet (lets call that 1,500 meters per second) we find that superman could wrap the world in seven hours. With that delay its quite likely that the candy would fall farther than superman can reasonably adjust for. I can't really say how far without knowing what a skittles terminal velocity is. Even if we assume that superman is many times faster than a speeding bullet we are still talking about hours of travel time, not The Flash's milliseconds.

So there's our answer. The Flash is fast enough to make a candy ring around the world, but isn't strong enough. Superman is strong enough, but not fast enough. Obviously we could keep going through the superhero pantheon, or argue about faster speeds for Superman or The Flash (some of Superman's comicbook feats require him to pass the speed of light), but I don't think that's the point. Based on my math, without time travel no super hero could create a ring out of candy (of course The Flash can apparently time travel, but that's cheating as far as I'm concerned).