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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.

What about the following subtraction?

$$\begin{align}&ab\\-&ba\\&\overline{c0}\end{align}$$
Problem ID: 277 (13 May 2006)     Difficulty: 1 Star

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