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