Special Numbers

Logic Level 3

Suppose \(M\) is a four-digit positive integer such that \(4M\) is also a four-digit number and \(4M\) has the same digits as \(M\), but in the reverse order. Find the sum of all possible \(M\).

As an illustration, if \(M\) is of the form \(\overline{abcd}\), then \(4M\) is of the form \(\overline{dcba}\), where \(a\), \(b\), \(c\) and \(d\) are digits.

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