The 3-Digit Number Trick: A Magical Mathematical Mystery!

Have you ever been amazed by a magic trick? Well, get ready to be amazed by a mathematical trick that seems like magic! It's called the 3-Digit Number Trick, and it's sure to leave you scratching your head and wondering how it works.

The Trick

Here's how the trick works:

1. Choose a 3-digit number. Make sure the first and last digits are different! For example, you could choose 523.
2. Reverse the digits. In our example, the reversed number would be 325.
3. Subtract the smaller number from the larger number. In our example, 523 - 325 = 198.
4. Add the digits of the result. In our example, 1 + 9 + 8 = 18.

The Mystery

No matter what 3-digit number you start with (as long as the first and last digits are different), you'll always end up with the same answer: 18! How is this possible?

The Explanation

The magic is actually in the math. Let's break it down:

Imagine your original 3-digit number is represented as abc, where a, b, and c are the digits. The reversed number would be cba.

When you subtract the smaller number from the larger number, you're essentially doing this:

  abc
- cba
-------

Let's look at the hundreds place. If a is larger than c, you'll have a - c in the hundreds place. But if c is larger than a, you'll need to borrow from the thousands place, which will make the hundreds place (a + 10 - c).

Similarly, the tens place will be either (b - b) or (b + 10 - b), and the units place will be either (c - a) or (c + 10 - a).

Notice that the hundreds and units place always add up to 9 or 19. In the case of 19, you carry the 1 over to the tens place, which also adds up to 9 or 19. And since 9 + 9 = 18, that's why you always end up with 18!

Try It Yourself!

Pick a few different 3-digit numbers and try the trick. You'll see it works every time! You can even impress your friends with this mathematical magic.

So, the next time you see a magic trick, remember that sometimes the most amazing things can be explained by simple math!