are consecutive digits. are also consecutive digits. are all different digits. If , find the sum of . (Note: are not necessarily consecutive digits.

Source: mathcontest.olemiss.edu 10/29/2007

**SOLUTION
**Let . Then, . Let , then .

Since is in the tens place and in the ones place, the value of is represented by

Since is in the hundreds place, in the tens place, and in the ones place, we represent the value of by

If , then we have the following equation:

Let’s try a few values for .

**a=0
**

Not a solution because it is conflicting with .

**a=1
**

Not a solution because the left side is even but the right side is odd.

**a=2
**

**Check
**

?

YES

Thus, .

**Answer**: 24.

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