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## 'Always a Multiple?' printed from http://nrich.maths.org/

Watch the video to see Charlie's number trick.

*If you can't play the video, you can read a description here.*

Try a few examples for yourself. Do you always get a multiple of 11?

Can you explain why?

Alison and Charlie came up with their own explanations:

*If you can't play the videos, you can read a description here.*

**Here are some similar number tricks.**

**Can you use Charlie's or Alison's representation to explain how they work?**

- Take any two-digit number. Reverse the digits, and subtract your answer from your original number. What do you notice?

- Take any two-digit number. Add its digits, and subtract your answer from your original number. What do you notice?

- Take any three-digit number. Reverse the digits, and subtract your answer from your original number. What do you notice?

- Take any five-digit number. Reverse the digits, and subtract your answer from your original number. What do you notice?

** **

Once you've been able to explain what is going on above, you should be able to explain why many other similar tricks work.

Here is a selection you might like to try:

Special Numbers

Think of Two Numbers

Legs Eleven

Puzzling Place Value