Find the sum of the digits in the expression .
Source: NCTM Mathematics Teacher, December 2005
If we multiply the numbers by hand, we have the following addition
The sum of the digits equals .
Let and .
We have the following subtraction
If we add the digit in the first column to the digit in the tenth column and so on, we have
This is true for any random 9-digit number, for example
In fact, the number is not necessary in this problem; any 9-digit number that is a multiple of will do.