Mathematical Improbability? How Santa Delivers All Those Toys

Santa Math

Write a holiday blog, and make it appealing to engineers. That was my assignment for this month. I thought about doing the usual fare, top 10 gifts and best-of-the-year lists, but that’s too easy.

Instead, I’m going to focus on something much more pressing: Does Santa Claus really exist? And if so, how can he possibly deliver all those toys by himself in a single night?

It turns out there’s some real math being done to answer this question, although nobody seems to want to own up to it.

Let’s start with the basics:

There are about 378 million Christian children in the world, or 15 percent of the two billion or so people on the planet who are under 18. At an average of 3.5 children per household (assuming at least one child per family was nice and not naughty), Santa Claus would have to visit 108 million homes in the 31 hours of darkness (allowing for time zones and the rotation of the globe) on Christmas night.

This little sum is all part of an elaborate calculation making the rounds in cyberspace that considers every statistical angle of the holiday. Santa, these computations conclude, has one-one hundredth of a second to land on each roof, bound down each chimney, twinkle his eyes, shake his belly like a bowlful of jelly, fill the stockings, grab the milk and cookies, lay his finger aside of his nose, rise back up the chimney, spring to his sleigh and fly away.

Then Santa has to travel an average of eight-tenths of a mile over the river and through the woods to the next house and do it again (here assuming that each of those 108 million households are evenly distributed). Total distance? Seventy-five and a half million miles. Velocity? Six hundred and fifty miles per second, or a jingle-bell-rockin’ 3,000 times the speed of sound. Faster than a bargain-hunter on Black Friday.

The origin of these calculations is as mysterious as Santa Claus himself, and harder to get to than the North Pole. No one seems to know who worked them out.

They appear most prominently on a web page that leads back to Newcastle University in the United Kingdom. The university has no idea where they came from. The professor of chemical engineering who posted them on the Newcastle website—and who now teaches in Singapore—says someone sent them to him in an email. He can’t remember who.

There’s another hint about where the Santa figures came from in a separate reference online that calls them “A Cal-Poly Engineer’s Anti-Santa Proof.” But no one at California Polytechnic State University at San Luis Obispo, or Cal Poly, ever heard of this.

A spokeswoman for the college pointed to the hyphen as a hint the piece originated with some Scrooge at the other Cal-Poly, or California State Polytechnic University in Pomona. There, a spokesman says there’s speculation it was written by an alumnus. Not a creature knows for sure, he says, or has any idea who that alumnus may have been.

Whoever it was, he or she also estimates Santa’s payload at more than 500,000 tons, based on the weight of just one medium-sized LEGO set for every child.

The typical earthbound reindeer can pull a maximum of 300 pounds (and only at 15 miles an hour, incidentally), meaning Santa’s sleigh would need 360,000 of them, adding 54,000 tons to the total weight and creating so much air resistance that at that speed, in addition to breaking the sound barrier, they would burst into flames.

You’ll forgive me if I prefer the journalist’s take on Christmas. In 1897 an editor at the New York Sun wrote to a skeptical girl named Virginia O’Hanlon:

“Alas! How dreary would be the world if there were no Santa Claus. There would be no childlike faith then, no poetry, no romance to make tolerable this existence. We should have no enjoyment, except in sense and sight. The eternal light with which childhood fills the world would be extinguished.”

Then again, there’s always the light of combusting reindeer. …

Photo: Flickr, DCA Santa Sleigh Rides for Everyone by Myrna Litt (CC BY 2.0)

About Jon Marcus

Jon Marcus is a writer based in Boston and a contributor to newspapers and magazines including the Washington Post, New York Times, Boston Globe Magazine, and the Times (U.K.) Higher Education magazine.
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