Penelope A. Carlson, the friendly and feisty 29-year-old midnight shift clerk at a popular Rte. 1 convenience store, was clubbed to death behind the store before dawn on Tuesday, Jan. 10.

Heidi A. Berg, a 30-year-old Internal Revenue Service employe who wrote children's books in her spare time, lived quietly and gave much of her comfortable income to the disadvantaged. She was shot six times in the back while jogging early on a Sunday morning, Aug. 12. She died where she fell.

Lisa A. Rinker, 18, left her mother's house late on the same night "for a breath of fresh air." She did not reappear that night, although she was seen the following night at a nearby convenience store. A week later her body was found in an area of dense brush beneath some powerlines near the Capital Beltway.

Her body was so badly decomposed that neither an autopsy nor microscopic examination of tissue have revealed why she died, but police have been investigating the case as if it were a murder.

As 1984 ends, the deaths of all three women remain mysteries. Despite interviewing hundreds of people in the unrelated cases, police say they are in many senses no closer to solving them than they were when the deaths occurred -- except that they know who can't tell them anything.

The slayings of Carlson and Berg and the apparent killing of Rinker, are Fairfax County's unsolved homicides from 1984.

County police officials say it is not unusual to close the year with one or two unsolved killings but that ending with three is uncommon. And the mystery surrounding these deaths -- two of them, especially -- is decidedly unusual in a county where the vast majority of homicides are related to domestic arguments.

"These are fascinating cases," said county prosecutor Robert F. Horan Jr., who added that they exhibit the sort of surface similarities typical of homicides that "go unsolved the longest."

All three women were dead when discovered, so none could tell police anything. In each case, the only other person to witness the deaths, investigators believe, was the person responsible. Despite rewards of $26,000 in the Carlson case and $12,500 in the Berg case, no one with valuable information has come forward, police said.

Seemingly the most mysterious of the deaths is the professional-style, ambush killing of the sweet-tempered Heidi Berg during her regular morning jog. She was carrying no money and she was not sexually assaulted.

"It's a distinct puzzle," said Horan. "The problem right now is the problem that existed from the very beginning: Why would anyone want to kill Heidi Berg? Of all the people who jog in Fairfax County, you wouldn't find many less likely to be the target of a homicide."

Berg, who lived at 8001 Chanute Place, tried, as an IRS employe,to persuade delinquent taxpayers to give the government what they owed.

But by all accounts she went about that delicate and potentially dangerous task in her typically mild-mannered and methodical way, "always seeming to leave the taxpayers with a good feeling, as though they had been helped out of the woods, helped out with their problems," as a coworker put it at the time.

A careful examination by both Fairfax and federal authorities of the tax cases on which Berg had worked turned up no one with any reason to kill her.

An equally exhaustive investigation of Berg's personal life, officials said, disclosed that Berg "was essentially an All-American girl" who lived quietly, Horan said.

Officials familiar with the investigation say it also turned up a boyfriend, previously unknown to even Berg's closest friends and family. He was cleared of suspicion, leaving investigators almost completely empty-handed.

No murder weapon has ever been found, and none of the people who jog regularly in the area of townhouses where Berg was killed saw or heard anything.

What police do know is that the person who killed Berg was very good with a gun, that the person was angry enough to empty the weapon and that the person was waiting for Berg just before 6:30 that bright, clear Sunday morning as she jogged a regular route near her home.

"Whoever it was emptied the gun, and that's a sure indication that whoever was doing the shooting was very, very serious about killing Heidi Berg," Horan said.

Four months after her death, however, investigators have uncovered so little useful information, Horan said, that they are beginning to take seriously an initial theory that Berg was killed mistakenly.

"When you have such a total absence of motive," Horan said, "you start looking around, and the obvious question is, is it possible someone set out to kill, but killed the wrong jogger?"

In contrast, Penelope Carlson's murder, the county's first in 1984, was brutally straightforward.

Carlson was the lone midnight clerk working at a busy 7-Eleven Store a block off Richmond Highway near the Huntington Metro Station, just a few blocks from her own home, early on that January morning.

About 3 a.m. someone entered the store and robbed it. Officials believe Carlson followed the robber outside. Horan speculates: "To stop the chase, he killed her."

Carlson was savagely beaten about the head and face, and the wooden club used to kill her was found with the body, according to officials familiar with the case.

Carlson, well known to regular late-night patrons of the store, was discovered by a delivery man who got suspicious when he found the store empty.

Horan is optimistic about closing the case. Robbery-murders, officials say, are rarely isolated crimes. The person who killed Carlson will do the same thing again, or will brag to somebody about this crime, and be caught, they predict.

"They'll catch that guy," said Horan. "These kind you normally do."

The death of Lisa Rinker is not classified as a homicide. Officials say they don't know how the teen-ager died and may never know. James Beyer, the medical examiner for Northern Virginia, told police her body was one of the most badly decomposed he had ever seen.

Still, officials believe, it is most likely she was slain.

Rinker's body was found by a family search party in a dense field between the Beltway and Lee Highway. In court documents, police say she was apparently "dragged to the final resting place," that she probably "died due to foul play and that the body was hidden to conceal homicide."

The principal clue in Rinker's death is a pair of pink flip-flop sandals she was wearing when she left her mother's home.

They were not found with the body, but were turned up by a friend of Rinker's about 100 yards away along Lee Highway, the day before the body was discovered.

According to court documents, the body showed they had been removed after Rinker had been dead quite some time. So, investigators say, whoever removed the shoes knew where Rinker's body was during the week she was missing.

The 22-year-old man who found those shoes along the road -- in an area police and family say had been searched several times before -- was initially the focus of the police investigation. In court documents police say he was "involved in the death of" Rinker. He was seen with her at a local convenience store, police say, the day after she disappeared.

The court affidavit says he "showed deception on all pertinent questions regarding the death of Lisa Rinker" on a polygraph test which he requested. But police have not charged him or anyone else in the case, and the man's attorney said last week he "denies any involvement in her death."

All three cases remain under active investigation by county police.