Using the five digits , and , what is the sum of all positive three-digit integers using these five digits? Please note that the same digit can appear more than once.

Source: mathcontest.olemiss.edu 4/15/2013

**SOLUTION**

This problem is similar to the problem titled “23567” dated 3/4/2013.

Let’s try a *smaller* problem to get an idea of what’s going on: sum of all three-digit positive integers formed from three digits: , and .

Total count of integers

The addition appears times contributing to the sum.

The addition appears times contributing to the sum.

The addition appears times contributing to the sum.

Sum of all three-digit positive integers formed from three digits: , and

Now apply the pattern to our problem: sum of all three-digit positive integers formed from the five digits: , and .

Total count of integers

The addition appears times contributing to the sum.

The addition appears times contributing to the sum.

The addition appears times contributing to the sum.

Sum of all three-digit positive integers formed from the five digits: , and

**Answer**: