The arithmetic mean of a set of nine different positive integers is 123456789. Each number in the set contains a different number of digits with the greatest value being a nine-digit number. Find the value of each of the nine numbers.

Source: mathcontest.olemiss.edu 1/26/2009

**SOLUTION
**Given a set of nine different positive integers, the arithmetic mean of the set is

Define the set of as follows:

Then,

Since we want the arithmetic mean to be 123456789, all we have to do is multiply each by 9.

**Answer**: 9; 99; 999; 9999; 99999; 999999; 9999999; 99999999; 999999999.

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