



 
Hi Megan, Many of these math tricks depend on casting out nines.
There is an explanation of why this works in our response to a question from Kelera. Kelera asked about divisibility by 9 and we used the example 5634 where r1 = r2 but the explanation is the same for any remainder. Here is your procedure.
Since the first two numbers have the same remainder when divided by 9 (they have the same digits) their difference will have a remainder of zero when divided by 9. So the number you have at this point is a multiple of 9.
Suppose the digit you circle is d then s is d less than a multiple of 9.
This is then s + d.
If you go to the Quandaries and Queries page and use the Quick Search for the term casting out 9 you will find some other math tricks that rely on casting out nines. Penny  


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