# Here's a simple magic trick anyone can do, thanks to a basic mathematic principle

Arthur Benjamin is a maths professor at Harvey Mudd College, but he’s got a side gig, too: as a magician.

His new book, “The Magic of Maths,” combines his two passions — which actually have a lot in common. “Mathematicians and magicians both want their audience to wonder: How did you do that?” Benjamin explains, in an interview with Deborah Kalb. “The magician keeps the method secret, but the mathematician wants you to understand.”

So first, here’s one of Benjamin’s magic tricks from his book, and — because he’s also a mathematician — we’ll also explain why it works:

Think of a number between 20 and 100. Got it? Now add your digits together. Now subtract the total from your original number. Finally, add the digits of the new number together.

What did you get?

Your result should be the number 9. (If it’s not, check your arithmetic.)

This is, in fact, an old trick, and there’s a simple reason why it works. Any two-digit number can be represented as a sum of 10*x + y, where x and y are both single-digit numbers. (Forty-two, for example, is [10*4] + 2.) The sum of those digits is x + y.

Now think about what the trick did: (10x + y) – (x + y). The answer to that will always be 9x, and as any elementary school child can tell you, the sum of the digits in any multiple of 9 is always 9.

Benjamin devotes a whole chapter to “The Magic of 9,” but that number is really just one small example of what he calls “the beautiful aspects of mathematics.”

“Mathematics is filled with magic like this,” he writes.

Now go try it on an unsuspecting friend — then show how it works.