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‘I told you that you were off the case.’

‘I know. But you will want to hear what I’ve got.’

Ólafur sighed. He was feeling the pressure — he needed something to break his way. He did want to know what Vigdís had got.

‘So tell me.’

Vigdís told him and Ólafur listened this time. Closely.

‘I need to go talk to this girl,’ Ólafur said.

‘Can I come?’ said Vigdís.

Ólafur opened his mouth to say no, but hesitated. ‘All right,’ he said, grabbing his coat. ‘But stay quiet. I’ll do the talking.’

Although it was only a two-minute walk to Halldór’s house, Ólafur took a police car and a uniformed officer. Gudrún answered the door and led them into the living room. A couple in their seventies sat on a sofa, staring at a skinny man of about twenty-three with a shaven head, wearing jeans and a stained T-shirt.

Sveinn. The fair curls of the teenager in the family photo had all gone.

Grief stalked the room. The family looked shattered, all four of them.

To Vigdís’s surprise, rather than demanding to speak to Gudrún immediately, Ólafur started with the grandparents. But it made sense: get as much background as possible before confronting a suspect.

First they spoke to the grandparents alone in the kitchen over cups of coffee. It turned out that they were Halldór’s parentsin-law — his own parents were both dead. They didn’t say much that the police didn’t know already. They had good things to say about Halldór and how he had brought up their grandchildren after their daughter’s death, although Vigdís got the impression that they were unhappy with his decision to move the family from Reykjavík to Raufarhöfn, about as far away from them as it was possible to go in Iceland.

Then it was Sveinn’s turn. He didn’t touch his coffee. He seemed nervous, fiddling with a cigarette, desperate to light up. His eyes darted around the room, from the detectives, to the door, to his cigarette. A strung-out junkie, Vigdís thought. She felt sorry for him — he must be feeling the pressure. She would have taken him outside so he could at least have a smoke, but that hadn’t seemed to have occurred to Ólafur, and she decided she should just keep quiet and be grateful that Ólafur had let her come along.

‘How were relations between you and your father?’ Ólafur began.

‘Not good,’ Sveinn replied unhappily. ‘Dad was really angry when I left university. Chemistry just wasn’t my thing and he didn’t understand that. And I’m sure you know I got busted for possession. Dad assumed I was a pusher. Which I’m not.’ He glared at Ólafur, daring him to contradict him. Vigdís wasn’t convinced. ‘I didn’t talk to him much after that.’

‘Did you talk to Gudrún?’ Ólafur asked.

‘Yeah. Not often. But every now and then.’

‘And how was the relationship between her and her father?’

‘Oh, Gudrún is a good girl,’ Sveinn said. ‘You can tell that just from looking at her. Works hard, passes exams, has nice clean boyfriends. Dad used to point out to me what a good girl she was.’

‘So no major arguments?’ Vigdís said.

‘Not until last week.’

‘Last week?’

‘Yeah. Gudrún called me. I’d seen the news about how Dad had shot the polar bear and was a big hero. I knew Gudrún would be upset about that; she’s a big Save the Whales supporter. And save the orangutan. And the chimpanzee. So I was pretty sure I could guess her attitude to Dad shooting a polar bear.’

Ólafur glanced at Vigdís. Gudrún hadn’t said anything about an argument.

‘So they had a fight?’ Ólafur asked.

‘A massive one. But it wasn’t just that Gudrún was upset that he had killed the polar bear. It was how he had done it.’

‘What do you mean?’

‘Gudrún has a friend who works in the petrol station — Lilja. Anyway, she told Gudrún she had spoken to an old farmer who lives on the other side of the river from where the bear was shot. Apparently, Dad let a little girl wander over to the bear so he could shoot it, rather than getting the little girl out of the way and letting the bear escape. Gudrún was horrified that Dad would use a child as bait like that.’ Sveinn broke the cigarette between his fingers and swore. ‘But I’m not surprised. If Dad thought he had a chance to be the guy who shot the polar bear, then he would take some big risks. And not just with his own life.’

‘Did your father teach you to shoot?’ Vigdís asked.

Sveinn frowned. ‘Yes.’

‘Were you any good?’

Sveinn nodded. ‘Not bad. Not as good as Dad, though. He was an excellent shot.’

‘What about Gudrún?’

‘She wasn’t a bad shot either, for a girl. Not as good as me.’ Sveinn’s brows knitted again. ‘Hold on. What are you suggesting?’

‘We’re just asking questions,’ Ólafur said.

‘No, you’re not. You’re suggesting that Gudrún shot Dad, aren’t you? Well, you know what? You’re out of your minds. You’ve met Gudrún. She would never shoot anyone, let alone Dad, no matter how angry she was with him.’

‘Just a couple more questions,’ said Ólafur.

‘No! No way! I’m not answering any more questions.’ Sveinn got to his feet and pulled out a packet of cigarettes. ‘You two are mental, you are. Bloody useless. All you cops are bloody useless. My dad was bloody useless.’ A tear appeared in his eye, but he rushed from the kitchen before it had a chance to escape. He threw open the back door and lit up outside.

Ólafur glanced at Vigdís. ‘I think we need to invite Gudrún down to the station, don’t you?’

Björn was waiting for them.

‘We heard back from the digital forensics guys in Reykjavík,’ he said. ‘Just a preliminary report, but it seems that between 14.38 and 17.53 on the afternoon of the murder, Martin — or someone acting as Martin — was playing Call of Duty online.’

‘Who with?’

‘Three people. Two Germans and a Dutchman.’

Ólafur glanced at Vigdís. ‘Sounds as if Martin may be telling the truth. He was playing a computer game when the shot was heard at about five or five-fifteen.’

Vigdís’s heart had leaped at the news, but she was determined not to let it blind her. She needed her head to be in control.

‘Possibly,’ she said. ‘Alex may have gone out and shot Halldór while Martin was playing the game. Or Martin may have constructed an alibi somehow with some German friends.’

‘Björn, see what the digital guys can do to confirm that he really was online. And get the Europol people in Reykjavík to get in touch with Germany. We need real detectives to talk to real people about this, not online bullshit.’

‘It will take a while to go through Europol.’

‘Which is why we need to get on to it quickly.’

‘Yes, Ólafur!’

‘Now, let’s talk to Gudrún.’ Ólafur hesitated. ‘And Vigdís. I’ll lead, but if you want to ask something, do.’

Halldór’s daughter looked alone and vulnerable in the interview room. Ólafur switched on the recorder and introduced himself, Vigdís, the uniformed officer and Gudrún.

‘Why am I here?’ Gudrún said. She looked scared.

‘Because you lied to us,’ said Ólafur.

‘Lied? What do you mean?’

‘You didn’t tell us that you had left university two days early to try to save the mother polar bear. Or that you had had a big argument with your father just before he died.’

The anxiety on Gudrún’s face ratcheted up. ‘Did my brother tell you this?’

‘Yes. And your tutor at the university. But the question is, why didn’t you tell us?’

Gudrún lowered her eyes to the desk.