Find the sum of all positive three-digit integers formed from the five digits: , and . The same digit can appear more than once.

Source: mathcontest.olemiss.edu 3/4/2013

**SOLUTION**

Let’s try a *smaller* problem to get an idea of what’s going on: sum of all positive integers formed from three digits: 2, 3, and 6.

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 positive integers formed from three digits: , and

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

**Answer**:

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