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

**SOLUTION**

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

**Answer**:

### Like this:

Like Loading...

*Related*

## About mvtrinh

Retired high school math teacher.