Find the sum of the digits in the expression .

Source: NCTM Mathematics Teacher, December 2005

**SOLUTION**

If we multiply the numbers by hand, we have the following addition

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The sum of the digits equals .

**Answer**:

**Alternative solution**

Let and .

We have the following subtraction

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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

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In fact, the number is not necessary in this problem; any 9-digit number that is a multiple of will do.

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