He woke with a start gasping for breath and stared into space while he collected himself. He called out to Eva Lind but received no reply. He walked to her room but sensed the emptiness there before he even opened the door. He knew she had left.

After examining the register of the inhabitants of Husavik, Elinborg and Sigurdur Oli had compiled a list of 176 women who were potential victims of rape by Holberg. All they had to go on was Ellidi’s word that it had been “the same sort of job", so they used Kolbrun’s age as a reference with a ten-year deviation either side. On first examination it emerged that the women could be roughly divided into three groups: a quarter of them still lived in Husavik, half had moved to Reykjavik and the remaining quarter was scattered throughout Iceland.

“Enough to drive you mad,” Elinborg sighed, looking down the list before she handed it to Erlendur. She noticed he was scruffier than usual. The stubble on his face was several days old, his bushy ginger hair stood out in all directions, his tatty and crumpled suit needed dry-cleaning: Elinborg was wondering whether to offer to point this out to him, but Erlendur’s expression didn’t invite any joking.

“How are you sleeping these days, Erlendur?” she asked guardedly.

“On my arse,” Erlendur said.

“And then what?” Sigurdur Oli said. “Should we just walk up to each of these women and ask if they were raped 40 years ago? Isn’t that a bit… brash?”

“I can’t see any other way to do it. Let’s start with the ones who’ve moved away from Husavik,” Erlendur said. “We’ll start looking in Reykjavik and see if we can’t gather any more information about this woman in the process. If that stupid bugger Ellidi isn’t lying, Holberg mentioned her to Kolbrun. She may well have repeated it, to her sister, maybe to Runar. I need to go back to Keflavik.”

“Maybe we can narrow the group down a bit,” he said, after a moment’s thought.

“Narrow it down? How?” said Elinborg. “What are you thinking?”

“I just had an idea.”

“What?” Elinborg was impatient already. She’d turned up for work in a new, pale green dress suit that no-one seemed likely to pay any attention to.

“Kinship, heredity and diseases,” Erlendur said.

“Right,” Sigurdur Oli said.

“Let’s assume Holberg was the rapist. We have no idea how many women he raped. We know about two and actually about only one for certain. Even though he denied it, everything points to the fact that he did rape Kolbrun. He was Audur’s father, or, at least, we should work on that assumption, but he could equally have had another child with the woman from Husavik.”

“Another child?” Elinborg said.

“Before Audur,” Erlendur said.

“Isn’t that unlikely?” Sigurdur Oli said.

Erlendur shrugged.

“Do you want us to narrow the group down to women who had children just before, what was it, 1964?”

“I don’t think that would be such a bad idea.”

“He could have kids all over the place,” Elinborg said.

“True. He didn’t necessarily commit more than one rape either so it’s a long shot,” Erlendur said. “Did you find out what his sister died of?”

“No, I’m working on it,” Sigurdur Oli said. “I tried to find out about their family, but nothing came out of it.”

“I checked on Gretar,” Elinborg said. “He disappeared suddenly, like the ground had opened up and swallowed him. No-one missed him in the slightest. When his mother hadn’t heard from him for two whole months she finally phoned the police. They put his picture in the papers and on TV but drew a blank. It was in 1974, the year of the big festival to commemorate the settlement of Iceland. In the summer. Did you go to the festival at Thingvellir then?”

“I was there,” Erlendur said. “What about Thing-vellir? Do you think that’s where he went missing?”

“Perhaps, but that’s all I know,” Elinborg said. “They made a routine missing-persons investigation and talked to people his mother knew that he knew, including Holberg and Ellidi. They questioned three others too but no-one knew anything. No-one missed Gretar except his mother and sister. He was born in Reykjavik, no wife or children, no girlfriend, no extended family. The case was left open for a few months and then it just died. He was 34.”

“If he was as pleasant as his mates Ellidi and Holberg, I’m not surprised nobody missed him,” Sigurdur Oli said.

“Thirteen people went missing in Iceland in the 1970s when Gretar disappeared,” Elinborg said. “Twelve in the 1980s, not counting fishermen lost at sea.”

“Thirteen disappearances,” Sigurdur Oli said, “isn’t that rather a lot? None of them solved?”

“There doesn’t have to be anything criminal behind it,” Elinborg said. “People disappear, want to disappear, make themselves disappear.”

“If I understand correctly,” Erlendur said, “the scenario is like this: Ellidi, Holberg and Gretar are having a night out at a dance in the Cross one weekend in the autumn of 1963.”

He saw that Sigurdur Oli’s face was one huge question mark.

“The Cross was an old military hospital post that was converted into a dancehall. They used to hold really raunchy dances there.”

“I think that was where the Icelandic Beatles started playing,” Elinborg interjected.

“They meet some women at the dance and one of the women has a party at her house afterwards,” Erlendur went on. “We need to try to find these women. Holberg walks one of them home and rapes her. Apparently he’d played the same trick before. He whispers to her what he did to another woman. She might have lived in Husavik and in all likelihood never pressed charges. Three days later Kolbrun has finally plucked up the courage to report the crime but runs into a policeman who has no sympathy for women who invite men in after a dance and then shout rape. Kolbrun has a baby girl. Holberg could have known about the baby, we find a photo of her gravestone in his desk. Who took it? Why? The girl dies from a fatal illness and her mother commits suicide three years later. Three years after that, one of Holberg’s mates disappears. Holberg is murdered a few days ago and an incomprehensible message is left behind.

“Why was Holberg murdered now, in his old age? Was his attacker connected to this background? And, if so, why wasn’t Holberg attacked before? Why all the wait? Or didn’t his murder have anything to do with the fact, if it is a fact, that Holberg was a rapist?”

“It doesn’t look like premeditated murder, I don’t think we can ignore that,” Sigurdur Oli interjected. “As Ellidi put it, what kind of wanker uses an ashtray? It’s not as if there was a long historical build-up to it. The message is just a joke, indecipherable. Holberg’s murder doesn’t have anything to do with any rape. We should probably be looking for the young man in the green army jacket.”

“Holberg was no angel,” Elinborg said. “Maybe it’s a revenge murder. Someone probably thought he deserved it.”

“The only person we know for certain who hated Holberg is Kolbrun’s sister in Keflavik,” Erlendur said. “I can’t imagine her killing anyone with an ashtray.”

“Couldn’t she have got someone else to do it?” said Sigurdur Oli.

“Who?” Erlendur asked.

“I don’t know. Anyway, I’m coming round to the idea that someone was prowling around the neighbourhood planning to break in somewhere, burgle the place and maybe smash it up, Holberg caught him and got hit over the head with the ashtray. It was some junkie who couldn’t tell his arse from his elbow. Nothing to do with the past, just the present. Reykjavik the way it is these days.”

“At least, someone thought the right thing to do was to bump him off,” Elinborg said. “We have to take the message seriously. It’s no joke.”

Sigurdur Oli looked at Erlendur. “When you talked about wanting to know precisely what the girl died of, do you mean what I think you mean?” he asked.