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NRICH: Always a Multiple?

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens…

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:

Here is a selection you might like to try:

Age 11 to 14

Math Topics
Algebra & Pre-Algebra, Linear Equations
Middle School, High School, Educator

## Organization

NRICH (University of Cambridge)

Challenge