What is the sum of all the positive three-digit integers that can be formed from the digits , and ? Note that the same digit can appear more than once.
Source: NCTM Mathematics Teacher, February 2006
We can make different three-digit integers from , and
Since each integer has digits, we have a total of digits which we are going to distribute evenly among columns: the column, the column, and the unit column. Thus, each column has digits.
If we divide the 125 digits evenly among the , and , each digit will appear times in each column.
Sum of each column equals
When we allow for place value, the sum of the integers equals