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# Digit Addition

I think you will always get back to your original number, because adding 9 is the same as adding 10 and subtracting 1.
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Age 5 to 11

Challenge Level

*Digit AdditionÂ printable sheet*

Here's a maths trick to try:

- Think of one of the numbers from 1 to 9.
- Add 9 to your number.
- Add the digits of your answer together. What is your new number?

What do you notice?

Try the trick again with a new starting number from 1 to 9. What do you notice now?

**Will this always happen if you start with a number from 1 to 9?**

Jonas tried the trick with a few different numbers. He said:

I think you will always get back to your original number, because adding 9 is the same as adding 10 and subtracting 1.

**Do you agree with Jonas? Can you help him explain what isÂ happening?
Can you explain the trick in a different way?**

Lee was writing all the counting numbers from 1 to 20. She stopped for a rest after writing seventeen digits. What was the last number she wrote?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?