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# Always a Multiple?

## You may also like

### Summing Consecutive Numbers

### Always the Same

### Fibs

Links to the University of Cambridge website
Links to the NRICH website Home page

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Age 11 to 14

Challenge Level

*Always a Multiple? printable worksheet*

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:

The Number Jumbler

Special Numbers

Think of Two Numbers

Legs Eleven

Puzzling Place Value

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

The well known Fibonacci sequence is 1 ,1, 2, 3, 5, 8, 13, 21.... How many Fibonacci sequences can you find containing the number 196 as one of the terms?