The woman was related to at least two of the three children.
Was she their doting mother? An adoring aunt?
Or, given her relative youth, perhaps a much older sister?
"That leaves you with so many possibilities," says New Hampshire State Police Sgt. Joe Ebert.
All four females are long dead, their bodies crammed into two 55-gallon barrels, the first barrel discovered by a hunter in 1985, the other 15 years later.
They have never been identified.
Now, there's a new push to solve a cold case that has stymied determined investigators.
This week, the National Center for Missing & Exploited Children, after a request from state police, released new 3-D facial reconstructions of the four victims. They provide more details than previous images.
Investigators hope that someone, by looking at gaps in their teeth, thickness of lips, the length of their hair or other features, will make a connection.
"The right person is going to see it," says Angela Williamson, director of the center's unknown victim identification team.
Seemingly endless questions and possible scenarios swirl around investigators who have sifted through hundreds of tips or leads over the years.
Is this a domestic case, or a professional hit? How did the barrels come to be on a wooded lot near a state park in Allenstown, New Hampshire?
Were the four transients? Could they have lived on a commune? Did they live in other state or country?
Police have no missing persons report associated with the mysterious case.
Ebert, in an interview with CNN on Friday, said he has been open to theories and new evidence since he joined the case a few years ago. He's certain of one thing.
"I believe that there is somebody who knows who these children are and knows what happened to them."
Two horrifying discoveries
During deer season in 1985, a hunter made a grisly discovery on a parcel of private property near Bear Brook State Park, known for its bogs, lakes and trails.
A steel drum contained the remains of the woman, estimated to be between ages 23 and 33, and the eldest girl, who was between 5 and 11. Original reports indicated they died of blunt-force trauma. Investigators later determined they were related in some way.
State police, who handle nearly all homicide investigations in New Hampshire, notified the National Crime Information Center (NCIC), a computerized index that includes such reports.
It was believed then that the victims might be a mother and child.
"They came to every person's door and asked, 'Have you heard anything, if you knew anyone that's missing?' " Allenstown resident Andrea Kelly told told CNN New Hampshire affiliate WMUR this week. '"No, we haven't heard anything.'"
Within one day of the discovery of the bodies, state police were called in to investigate an apparently unrelated slaying of a man in nearby Hookset. Suddenly, that murder became the priority of the police force.
"It took a great number of resources," Ebert says of the Hookset investigation. That murder was finally solved eight years ago.
New Hampshire, with a population of about 1. 3 million, sees an average of only 20 to 30 homicides a year, according to Ebert. About half are domestic incidents.