Distinct Sum

Number Theory Level 3

Let the 10 letters \( A\) to \(J\) represent each of the digits \(0\) to \(9\) (not necessarily in order.

What is the minimum value of \( \overline{A} + \overline{BC} + \overline{DEF} + \overline{GHIJ} \)?

\( \overline{ABC} \) refers to reading the number in decimal base. \(\overline{ABC} = 100A + 10B + C \), and not \( A \times B \times C\).

Details and assumptions

The letters represent digits. Any of them can be any of the digits.


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