Hemberg came out to Arlöv a little after midnight. At that point the forensic investigation was already under way. Wallander had sent Andersson home in his car without giving him a better explanation of what had happened. Then he had stood by the gate and waited for the first police car to arrive. He had spoken with a detective inspector by the name of Stefansson, who was his own age.

'Did you know her?' he asked.

'No,' Wallander answered.

'Then what are you doing here?'

'I'll explain that to Hemberg,' Wallander said.

Stefansson regarded him sceptically but did not ask any further questions.

Hemberg started by walking around the kitchen. He stood in the doorway for a long time, simply looking at the dead woman. Wallander saw how his gaze travelled around the room. After standing there for a length of time he turned to Stefansson, who appeared to have great respect for him.

'Do we know who she is?' Hemberg asked.

They went into the living room. Stefansson had opened a handbag and spread some identifying documentation on the table.

'Alexandra Batista-Lundström,' he answered. 'A Swedish citizen, but born in Brazil in 1922. It seems she came over right after the war. If I have understood this correctly, she was married to a man named Lundström. There are divorce papers here from 1957. But at that point she already had citizenship. She gave up the Swedish surname later on. She has a post office savings account under the name of Batista. No Lundström.'

'Did she have any children?'

Stefansson shook his head.

'It doesn't seem like anyone else lived here with her. We've talked to one of the neighbours. Apparently she has lived here since the place was built.'

Hemberg nodded and then turned to Wallander.

'Let's go up a floor,' he said, 'and let the technicians work undisturbed.'

Stefansson was on his way to join them, but Hemberg held him back. There were three rooms upstairs. The woman's bedroom, a room that was basically empty except for a linen cupboard, and a guest room. Hemberg sat down on the bed in the guest room and indicated to Wallander that he should sit in the chair in the corner.

'I really only have one question,' Hemberg began. 'What do you think it is?'

'You're of course wondering what I was doing here.'

'I would probably put it more forcefully,' Hemberg said. 'How the hell did you end up here?'

'It's a long story,' Wallander said.

'Make it short,' Hemberg replied. 'But leave nothing out.'

Wallander told him. About the betting forms, the telephone calls, the taxicabs. Hemberg listened with his eyes stubbornly directed at the floor. When Wallander finished, he sat for a while without saying anything.

'Since you've found a murder victim, I naturally have to praise you for it,' he started. 'There also seems to be nothing wrong with your determination. Nor has your thinking been completely wrong. But apart from these things, it goes without saying that your actions have been completely unjustifiable. There is no room in police work for anything resembling independent and secret surveillance, with detect ives assigning themselves their own work. I say this only once.'

Wallander nodded. He understood.

'Do you have anything else to tell me? Apart from what led you here to Arlöv?'

Wallander told him about his visit to Helena at the shipping company.

'Nothing more?'

'Nothing.'

Wallander was prepared for a lecture. But Hemberg simply got up from the bed and nodded for him to follow suit.

On the stairs he stopped and turned round.

'I looked for you today,' he said. 'To tell you the results of the weapons inspection. There was nothing unexpected in the report. But they said you had called in sick?'

'I had a stomach ache this morning. Stomach flu.'

Hemberg gave him an ironic look.

'That was quick,' he said. 'But since you seem to have got better you can stay here tonight. You may learn something. Don't touch anything, don't say anything. Just make mental notes.'

At half past three the woman's body was taken away. Sjunnesson had arrived shortly after one. Wallander wondered why he didn't seem at all tired even though it was the middle of the night. Hemberg, Stefansson and another detective had methodically searched the apartment, opened drawers and cupboards, and found a number of things that they put out on the table. Wallander had also listened to a conversation between Hemberg and a medical examiner called Jörne. There was no doubt that the woman had been strangled. In his initial examination Jörne had also found signs that she had been struck on the head from behind. Hemberg explained that what he most needed to know was how long she had been dead.

'She has probably been sitting in that chair for a couple of days,' Jörne answered.

'How many?'

'I won't hazard a guess. You'll have to wait until the autopsy is complete.'

When the conversation with Jörne was over, Hemberg turned to Wallander.

'You understand, of course, why I asked him this,' he said.

'You want to know if she died before Hålén?'

Hemberg nodded.

'In that case it would give us a reasonable explanation for why a person had taken his own life. It is not unusual for murderers to commit suicide.'

Hemberg sat down on the couch in the living room. Stefansson was standing out in the hall, talking to the police photographer.

'One thing we can nonetheless see quite clearly,' Hemberg said after a pause. 'The woman was killed as she sat in the chair. Someone hit her on the head. There are traces of blood on the floor and on the wax tablecloth. Then she was strangled. That gives us several possible points of departure.'

Hemberg looked at Wallander.

He's testing me, Wallander thought. He wants to know if I measure up.

'It must mean that the woman knew the person who killed her.'

'Correct. And more?'

Wallander searched his mind. Were there any other conclusions to be drawn? He shook his head.

'You have to use your eyes,' Hemberg said. 'Was there something on the table? One cup? Several cups? How was she dressed? It is one thing that she knew the person who killed her. Let us for the sake of simplicity assume it was a man. But how well did she know him?'

Wallander understood. It bothered him that he had initially missed what Hemberg had been getting at.

'She was wearing a nightgown and robe,' he said. 'That's not something you wear with just anyone.'

'How did her bed look?'

'It was unmade.'

'Conclusion?'

'Alexandra Batista may have had a relationship with the man who killed her.'

'More?'

'There were no cups on the table, but there were some unwashed glasses next to the stove.'

'We will examine them,' Hemberg said. 'What did they drink? Are there fingerprints? Empty glasses have many exciting things to tell us.'

He rose heavily from the couch. Wallander suddenly realised that he was tired.

'So we actually know a great deal,' Hemberg continued. 'Since there are no signs of an intruder we will work with the hypothesis that the murder was committed under the auspices of a personal connection.'

'That still doesn't explain the fire at Hålén's place,' Wallander said.

Hemberg studied him critically.

'You're getting ahead of yourself,' he said. 'We are going to move forward calmly and methodically. We know some things with a great deal of certainty. We proceed from these things. What we do not know, or what we cannot be sure of, will have to wait. You cannot solve a puzzle if half of the pieces are still in the box.'

They had reached the hall. Stefansson had finished his conversation with the photographer and was now talking on the phone.