Mistakes do give rise to problems

Number Theory Level 4

\[\large \dfrac{BOB}{DAD} = 0.HULKHULKHULK\dots\]

In the above cryptogram \(BOB\) is divided by \(DAD\) to obtain a recurring decimal \(0.HULKHULKHULK\dots\) which has repeating period of four digits \((HULK)\). Furthermore, \( \gcd(BOB, DAD) = 1 \).

Compute \(B+O+D+A+H+U+L+K\).

Details And Assumptions:

  • \(B,O,D,A,H,U,L,K\) represent distinct digits.

  • \(BOB\) and \(DAD\) are three digit numbers.

Recently I was attempting Nihar's Problem and misread 1 statement of his question. This alternate problem is shown here since I'm a crappy person and don't want my efforts to be going down the drain.

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