The First Half:
Lucy Valdon gets a phone call- there is a baby on her doorstep and it is her late husband's child. The question is who is the mother, and is it her husband's child? Mrs. Valdon expects Nero Wolf to find out. Wolf wants lunch, so it is to Archie to conduct the interviews. Mrs. Valdon says that she had no enemies, and her only obsession is killer fog. She provides a list of women who may have been the mother, which is distressingly long, and the items that came with the baby. She also seems to rather like Archie and to her surprise flirts with him.
The baby cloths have one distinguishing characteristic: handmade horsehair buttons. His search is fruitless (despite visiting the Button Man, who had donated buttons to five museums in nine countries), but it is established that they were hand made and would have taken hours. Wolf has Archie put in add in the paper to find the maker, which flushed out a point to Anne Tenzer, a real knockout. Her Aunt Ellen had made the buttons, and when she wasn't making buttons, she was making a living taking in babies. She also knows who the mother is, but is killed before they find out from her who it is.
With that line of questioning closed they want to bring in the late Richard Valdon's four best friends to get a full list of possible candidates for the mother. They ask for Mrs. Valdon's help on the names which she gives, providing that Archie start calling her Lucy. Mr. Wolf is less than amused by the familiarity, but they get the names and three of them Willis Krug, Julian Haft and Leo Bingham agree to help. The fourth, Manny Upton, refuses and leaves in a huff. There are 148 possibilities for the mother. With the names and the client's hard earned inherited cash, the Great Mother Hunt begins. 26 Days, four countries and $8,670 later they had accounted for four mystery babies, seven women who had been away the month the baby was born, and the non involvement of the other 141 women. They were also right back at square one. On the upside, Archie's relationship with Lucy was continuing to improve.