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# How to Amaze Your Friends With Number Tricks

Easy number tricks to impress your friends.

By
Jason Marshall, PhD,
August 17, 2012
Episode #071

Page 1 of 3

There are tons of practical, real-world applications of math—building skyscrapers, launching satellites, programming video games and movie special effects, and running banks and stock markets. There are also tons of applications of math that aren’t necessarily as practical, but are just as much—if not even more—fun. So today we’re going to focus on this purely fun side of math and talk about a few number tricks that you can use to amaze your friends.

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## How to Perform a Number Trick With Years

Start by taking the last two digits from the year in which you were born and then add it to the age you’re going to be at the end of this year. Go ahead and figure out what that number is for you. Again, it’s the last two digits of the year in which you were born plus the age you’ll be at the end of this year. I’m willing to bet that you got an answer of 111, right? How did I know that? Magic? Well, no...it’s not magic. It’s math.

This trick does seem pretty impressive, right? Since I have no idea what year you were born, it means this trick must work for everybody on Earth! Well, actually, it works for everybody who was born in the 20th century. If you were born after the turn of the new millennium and you do this trick, you’ll always get the answer 11 instead of 111. But why?

## How the Trick With Years Works

Here’s how it works: Let’s assume you were born in the 1900s. Then you can think of the last two digits of the year in which you were born as the answer to the problem 19xx – 1900 (where 19xx is your birth year). And you can think of the age you’re going to be at the end of this year (which is 2011) as the answer to the problem 2011 – 19xx. Now, you’ll recall that the instructions were to add the last two digits of your birth year, which we’ve seen can be written 19xx – 1900, to the age you’ll be at the end of this year, 2011 – 19xx.

And that’s just 19xx – 1900 + 2011 – 19xx.

Do you see what happened there? We can make it a bit clearer by using the commutative and associative properties of addition (and the fact that subtracting a number is the same as adding its negative) to rearrange the problem to read:

19xx – 19xx + 2011 – 1900

Now do you see what’s happening? The year of your birth—the only thing in the problem that changes from person to person—actually cancels out in the arithmetic: 19xx – 19xx = 0. So when we add the two pieces of the puzzle together (the last two digits of your birth year and the age you’ll be at the end of this year) we end up with 2011 – 1900…which is always equal to 111—no matter what year of the 1900s you were born.

Once you break it down, it’s clear this trick isn’t magic. But now that you know how it works, feel free to pretend that it is and use it to amaze your friends.

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