**Think of a two-digit number.
Reverse the digits and add your answer to your original number. **

*For example, Alison chose 42 and added 24 to get 66.*

Try a few examples.

Can you explain why your answer is always a multiple of 11?

Alison and Charlie came up with their own explanations:

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

Alison arranged multilink to show **four tens** and **two units** for 42, and **two tens** and **four units** for 24.

She then put the **four units** with the **four tens**, and the **two units** with the **two tens**, giving six lots of eleven.

Charlie imagined a two-digit number $ab$, where $a$ represents the number in the tens column, and $b$ respresents the number in the units. This can be written as $10a+b$. Similarly, $ba$ can be written as $10b+a$.

Charlie added these together to get $11a+11b$, which he wrote as $11(a+b)$.

**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?

** Can you make up some number tricks of your own?**

## Comments

### THIS QUESTION

This is incredibly cool and fun to try out. I highly recommend.

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### This Question

This is really cool, I highly recommend it.

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### Really cool, easy to

Really cool, easy to understand

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### COOL

it is good and fun and easy to understand

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### it is always a multiple of 11

it is always a multiple of 11 because the reversed digits even it out, *eg.* 5+6 equals 11, and 60+50 equals 110

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