Maximum summed sub sequences with no two numbers sharing the same digit
05AB1E, 11 bytes

æʒ€ÙJDÙQ}OZ


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Explanation

æʒ      }    # filter the powerset of the input, keep only elements
  €Ù         # where each number with duplicate digits removed
    JDÙQ     # have different digits from the other numbers
         O   # sum each
          Z  # take max