A number theory problem by Jack Rawlin

Number Theory Level pending

You are told that a for a three digit number \(\overline{ABC}\)

\[\overline{ABC} - \overline{CBA} = -198\]

\[\overline{ABC} + B = 327\]

\[D = (A + 2B + 3C) - 14\]

Find \(\frac {\overline{DBAC}}{5}\)


Details and assumptions

  1. \(\overline{ABC} = 100A + 10B + C\)

  2. \(A\), \(B\), \(C\) and \(D\) are all positive integers under \(10\).

  3. \(A > 0\)

  4. \(\frac{\overline{DBAC}}{5}\) is an integer.

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