Certain approaches lead to an early total of nineteen people. The addition of nine sons, nine sisters, and one father produces that number. The structure of the sentence contains the source of the common error.
The riddle states that a man has nine sons. It states that each son has a sister. The wording does not specify separate sisters for each son.
All nine sons may share one sister. That possibility holds the key.
A careful breakdown follows.
Nine sons form the first group.
One sister forms the sibling shared