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Take any four-digit number.
Create a second number by moving the first digit to the 'back of the queue' and moving the rest along.
Now add your two numbers.
I predict your answer will be a multiple of 11...
Try it a few times. Is the answer always a multiple of $11$?
Can you explain why?
Click below to see what Samira noticed:
Click below to see what Jay noticed:
Do these observations help you to explain what's going on?
What if you start with a three-digit number?
Or a five-digit number?
Or a six-digit number?
Or a 38-digit numbers ... ?
Can you prove your findings?
You may be interested in this article on Divisibility Tests.
Click here for a poster of this problem.