What Are Happy Numbers?

This image shows some "happy numbers."

How can you tell if a number is "happy"? Take each digit and square it. Then add up the squares.

You'll get a new number. Add up the squares of the digits again.

Keep doing that... if you eventually get to 1, you have a happy number!

Here's what it looks like if you start with 44:

Happy Number Engine

Use the interactive below to save yourself some computation. Try entering numbers that are in the diagram above. Try numbers that are not. What do you notice? What do you wonder?

Enter a whole number up to 999,999.

Click "Go!" to see your number and the next number. Keep clicking "Go!" to get more numbers.

Click "Reset" to start with a new number. (Or just type a new number in the box and click "Go!".)

Click "Clear" to clear the results area.

When you are ready to explore further, click "Let's Go!"

(Warning! Spoilers ahead... Make sure you have investigated as much as you want on this page before you move on.)