How Much Weight Would Santa Gain From Eating Milk and Cookies at Every House He Visits?

Dave Consiglio:

This is a simple question for the Factor Label Method. This method, also known as dimensional analysis or unit analysis, make problems a breeze. I highly recommend it to anyone interested in doing seemingly hard math problems like this one. Here’s how you use it:

1. Write your given—in this case “1 Santa Claus”—on the left side of your paper
2. Write your desired answer—in this case “pounds”—on the right side of the paper
3. Make a chain of units from left to right (no numbers required).
4. Fill in the numbers
5. Multiply by all the tops
6. Divide by all the bottoms
7. Clean up

In just 7 simple steps you’ve got an answer. Here’s my answer. (Note: I assumed a cookie has 200 calories and a glass of milk has 100 calories. Your results will vary based on the type of cookie. I also assumed around 2 billion houses.) Here’s my Factor Label Method:

Answer: 400,000,000 pounds.

One of the best things about mathematics of this kind is that, by approximating in this way, you can see the magnitude of your answer. This answer is 400 million pounds, but it might be 300 or 500 million, depending on your assumptions. So what?

Well, while we may not know the precise answer, what we do know is that the answer is very large.

This kind of answer can be really helpful. You don’t always have to have the precise answer. A “good enough” answer can give you a pretty good idea of where you stand.

By the way: We’re assuming that Santa burns no calories during his trip. If he burns calories like a normal man his size and age, he will probably only gain around 399,999,999 pounds. But if Santa uses calories to propel his sleigh around the world (perhaps he has a “fat to magic” converter?), then he might be able to travel the whole world using only the calories from his cookies and milk and gaining no weight at all. Magic is a tricky thing to quantify.

But for the real world, the Factor Label Method is the next best thing to magic.

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