Santa could definitely visit all of those houses in one night

The non-believers out there will tell you that Santa would have to travel faster than light to reach every house in a single night, but that's just not true.

First of all, how long is a single night? The obvious answer is "around eight hours", after all Santa visits us when we're sleeping, and you're supposed to get around eight hours of sleep. That's not right though, because of time zones.

When it's midnight in Greenwich, it's 6:00 in Austin. Santa has six hours to deliver all the Greenwich presents before he ever has to worry about the Austin kids. If Santa starts at one end of the international date line and works his way westward throughout the entire planet, he'll have a full 24 hours to deliver all the presents, not eight!

He'll obviously have to go at approximately the same pace as the Earth's rotation, but Santa's magic. He's got abilities that surpass any technologies that we have today. Let's assume that he can go at 10% of the speed of light. Let's also define one "second" as the distance that the sun travels in the sky in a single second, or 1/86400 times the circumference of a given lattitude. Note that this is not the conventional definition of a "second" as a 1/60 "minutes", where one "minute" is 1/60 geographic degrees. Let's also assume that there is never more than one house within the same second and lattitude line.

These assumptions make our math quite easy. Just find out the distance that Santa will have to travel in a single second (geographic), and check if he could actually cover that distance in a single second (time). Because of that "single house" assumption, Santa will never have to double back within a single second. This means that Santa just has to travel half the circumference of the Earth and deliver all the presents along the way. The circumference of the Earth is 40,000 km, so in a single second Santa will have to travel 20,000 km. The speed of light is around 200,000300,000 (the original version of this article had a typo) km/s, so if Santa can travel at 10% of that he'll be able to deliver all of those presents.

Of course, I made quite a few assumptions throughout this. I have no doubt that Santa can travel at 10% of the speed of light. Particle accelerators can accelerate particles far faster than that, and Santa has something far more powerful than a particle accelerator - Christmas spirit.

The single house assumption is quite simple to dismiss as well. The surface area of a single second can be derived with calculus, but one second is 1/86400 the surface area of the Earth, so if we assume the Earth is a perfect sphere, then:

Area of one second =
1/86400 * Surface area of the Earth =
1/86400 * 4*pi*r^2 =
1/86400 * 4*pi*(4000km / 2*pi)^2 = 59 km^2

59 square kilometers is not very much. Manhattan has a population density of 28,872 people per square kilometer. If the entire planet was covered with the population density of Manhattan, there would be around 1.7 million people per second, which is equivalent to a person every 11 meters that Santa travels throughout the second. 11 meters is quite far, and the Earth is not more densly populated than Manhattan.

SIDE NOTE: The Kowloon Walled City was wild. There were 35,000 people in 26,000 square meters. That's 1.3 million people per square kilometer. You would have to stack over 46 Manhattans on top of each other to match that population density.

The only remaining assumption I can think of is that the Earth is evenly populated, but there is an eight hour window to get the houses in a given location. The worst possible "burst" of people that Santa could encounter is a large group of people concentrated along a single longitude line. This longitude line would have to have the same population as eight hours of Manhattan. That's 49 billion people, or over six times the world population.

In conclusion, Santa could definitely visit everybody's house in a single night, even if the entire Earth's surface area had the population density of Manhattan, and even if 50 billion people lived along a single longitude line thanks to time zones and Christmas spirit.