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Subtraction Surprise

Age 7 to 14 Challenge Level:
In the video below, Alison chooses some three-digit numbers and carries out some calculations which lead to a surprising result!

Watch the video. What do you notice?
Can you figure out the steps that Alison carries out in each calculation?

This video has no sound.
If you can't see the video, click below to see the steps and the examples Alison tried. 



Pick any three digit number.
Reverse the digits, so write your number back to front.
Subtract the smaller of your two numbers from the larger one.
Now reverse the digits of the answer you get.
Add the answer to its reverse.

  7 2 3
- 3 2 7
  3 9 6
+ 6 9 3
1 0 8 9
  8 5 6
- 6 5 8
  1 9 8
+ 8 9 1
1 0 8 9
  3 9 2
- 2 9 3
  0 9 9
+ 9 9 0
1 0 8 9

 



Choose some three-digit numbers of your own.
(Make sure the first and third digits are different)
Is there a pattern to all the answers?

Now watch the videos again. This time, all three subtractions are carried out at the same time.
You may wish to pause the video at certain points, or watch it several times.


What is the same in each example?
What is different?

Does every example lead to the same answer?
Can you use what you noticed in the video to prove it?