## Reverse Difference

#### Problem

Find the value of the digit $c$ in the following calculation.

\begin{align}&ab\\-&ba\\&\overline{c4}\end{align}

#### Solution

Writing $(10a + b) - (10b + a) = 9a - 9b = 9(a - b)$, we can see that the difference must be a multiple of nine.

The only 2-digit multiple of nine ending with the digit 4 is 54, hence \$c = 5.

\begin{align}&ab\\-&ba\\&\overline{c0}\end{align}