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The Math Behind Christmas Magic

Believe it or not, there’s math in the magic of the holidays! On December 24, Santa will put on his hat, hopefully remember his gloves (it’s cold out there) and make a trip around the world. He has to travel to far off lands and be back to the North Pole before Mrs. Claus wakes up.  How does he do it? By magic of course!

If Santa was a regular guy, could he pull off such a feat? Just for fun, let’s look at the math behind Christmas magic.

santa math holiday math

How Many Homes?

How many homes does Santa visit in one night? Assuming Santa only visits children under the age of 18, there are roughly 2 billion children in the world and approximately 15% of those children celebrate Christmas.  At an average rate of 3.5 children per household (with at least one good child in each house), according to the Mathematical Association of America, Santa would have to visit 108,000,000 individual homes.  We guess by the time he finishes his trip, he’s pretty full of sugar cookies.

How Much Time at Each Home?

Taking in all the different time zones and the rotation of the earth and also the logical conclusion that Santa would travel east to west, he would need to make 822.6 visits per second. So for each household that celebrates Christmas, Santa has 1/100th of a second to park his sleigh on the roof, slide down the chimney (assuming he doesn’t get stuck), fill the stockings, put the presents nicely under the tree (avoiding the barking dog), climb back up the chimney, get in the sleigh, exclaim “On Dasher” and move onto the next house.

But the Science of Santa Claus brings up a different point:

“Based on his advanced knowledge of the theory of relativity, Santa recognizes that time can be stretched like a rubber band, that space can be squeezed like an orange and that light can be bent,” Silverberg says. “Relativity clouds are controllable domains — rips in time — that allow him months to deliver presents while only a few minutes pass on Earth. The presents are truly delivered in a wink of an eye.”

How Many Reindeer?

If Santa hired regular reindeer from a local farm in the North Pole, he’d need a lot more than eight. According to the Mathematics of Santa Clause, if Santa used regular reindeer and they generated about 1 horsepower each, he would need 2 billion reindeer to pull his sleigh. And if the sleigh was hitched two-by-two it would reach from here to the moon and back twenty times.

But according to the  Science of Santa Clause, the reindeer don’t pull a sled full of toys:

His reindeer — don’t actually pull a sleigh loaded down with toys. Instead, each house becomes Santa’s workshop as he utilizes a nano-toymaker to fabricate toys inside the children’s homes.

Santa is high tech!

Track Santa’s Trip

Whether you think it’s magic or Santa is just really, really fast, you can track him with your kids. Find out where Claus is flying this Christmas Eve with the official NORAD Tracks Santa. Since 1955, the North American Aerospace Defense Command (NORAD) is the most trusted source to find updates on Santa’s trek around the world on Christmas Eve.

Have a truly magical holiday season! And don’t forget to ask Santa for a subscription to our online math game. It’s fun, educational, and he wouldn’t even have to carry it on his sleigh full of toys (wink, wink).

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