John Dickson Carr. And we mustn’t forget Sir Arthur Conan Doyle, of course, and his immortal Sherlock Holmes. And now, Sergeant Lee, you and I have a real life impossible mystery to solve.'

'So you now suspect foul play?' asked Sergeant Lee.

'How could it not be?' asked Inspector Zhang.

'But Mrs. Wong told you that she was going to kill herself, and then she did.'

'You think that she managed to drown herself as she fell? That is very unlikely. Impossible in fact.' He stood up. 'First we must return to the scene of the crime, because that is what I think we have now. A crime.'

Inspector Zhang drove them to River Valley and parked in a multi-storey car park. This time there was a doorman on duty and he buzzed them in. His name was Mr. Lau and he told the detectives that he worked from eight o’clock in the morning until six o’clock in the evening. He was in his sixties, a small man with a bald head and a mole the size of a small coin on his chin. Inspector Zhang showed him a photocopy of Mrs. Wong’s identity card. 'Has this lady ever visited anyone in the building?'

Mr. Lau licked his lower lip as he studied the photocopy, then he shook his head. 'I don’t think so,' he said.

'And there’s no CCTV in the building?'

'The residents didn’t want it,' he said. 'People like their privacy.'

'It would make our job easier if every building had CCTV,' said Inspector Zhang.

'I suppose you’d like them inside people’s homes, too,' said Mr. Lau.

'That might be going too far,' said Inspector Zhang, putting the photocopy into his pocket. 'Do you have a list of the occupants of the building?'

Mr. Lau bent down and pulled a clipboard from underneath the counter. The top sheet was a list of all the apartments, the names of the occupants and contact numbers. Inspector Zhang studied the list. 'Can I have a copy of this?'

'It’s the only copy I have,' said Mr. Lau. 'But there’s a photocopier in the office, I can make a copy for you.'

Inspector Zhang smiled. 'That would be very helpful, thank you.'

Mr. Lau went into the office and returned with a photocopied sheet that he handed to the inspector.

'We’ll be on the roof for a while,' said Inspector Zhang. 'Can you tell me, is the door to the roof ever locked?'

'It’s supposed to be,' said Mr. Lau. 'All the residents have keys, but often it gets left open.'

'So anyone could gain access?'

'I suppose so, yes.'

'Do you happen to know if it was locked last night?'

Mr. Lau shook his head. 'I was up three days ago and it was locked then, but I haven’t checked since. It’s a relaxation area for the residents; they can have barbecues up there if they want. It’s a pleasant place to sit, when it isn’t too hot. There’s a nice breeze up there, from the river.'

Inspector Zhang thanked him and then went up in the elevator to the tenth floor with Sergeant Lee. They went out onto the roof and over to the section of the railing that Mrs. Wong had fallen from. Inspector Zhang looked down at the street below. 'She was here when she was shouting,' he said. 'She was standing here, leaning against the railing.' He pointed down to the pavement far below. 'I was there with my wife. And four other people, all of us looking up. I tried to talk to her but all I could do was shout. I am not sure if she even heard me. She carried on shouting and more people stopped to look at her.'

'It was definitely her?'

'It was the same dress, that I’m sure off. Was it the same woman? How could it not be, Sergeant Lee? I saw her fall. I saw her hit the ground. We found her handbag up here with her ID card.' Inspector Zhang sighed. 'So how did she manage to drown between here and the ground?'

'It’s a mystery,' said Sergeant Lee.

Inspector Zhang beamed. 'Yes,' he said. 'It is.'

'Can you solve it, Inspector Zhang?'

'I hope so,' said the inspector. 'I really do.' He turned away from the railing. 'We have to ask ourselves why she came here,' he said. 'When it appeared to be suicide, where she was didn’t matter because she could have chosen any tall building. But if she didn’t kill herself, there must have been a reason why she came to this particular one.'

Sergeant Lee nodded. 'She came to see someone?'

'I think so,' said the inspector.

'Should we speak to the apartment owners?'

Inspector Zhang scratched his chin. The building was ten stories high with four apartments on each floor. It would only take a few hours to knock on all the doors. But if the killer lived in one of the apartments, visiting them would only tip them off that the police were on the case. 'Let’s go and look at her belongings first,' he said. 'That might make things clearer.'

During Inspector Zhang’s time with the Singapore Police Force, the Forensic Medicine Division had evolved from the Centre for Forensic Medicine and before that the Department of Forensic Medicine. It was a case of a rose by any other name, Inspector Zhang knew, because its role hadn’t changed — it provided forensic expertise to the State Coroner and technical support to the police. They drove to Outram Road and parked close to Block 9 of the Health Sciences Authority, which housed the mortuary.

They showed their warrant cards to a bored security guard and went through to an office where Dr. Choi was waiting. 'Good morning, Inspector Zhang,' she said. She smiled showing perfect white teeth.

'Good morning, Dr. Choi.' He waved a hand at his sergeant. 'This is Sergeant Lee. She is assisting me on this case.'

A white-coated assistant came in carrying a large cardboard box which he placed on a stainless steel table. 'These are Mrs. Wong’s personal effects and clothing,' said Dr. Choi. 'Do you want to look at the body?'

'I don’t think so,' said Inspector Zhang. 'But you can answer one question for me. The water in Mrs. Wong’s lungs, was it sea water?'

Dr. Choi shook her head. 'It was definitely not salt water,' she said. 'There were no traces of salt. It was plain water.' She looked at her watch. 'I have an autopsy that has to be done before lunch,' she said. 'Please just leave the box here when you’ve finished and I’ll collect it.'

Sergeant Lee opened the box as Dr. Choi left the room. She took out the Louis Vuitton handbag and placed it on the table, followed by the dead woman’s dress, shoes and underwear. She started to open the handbag, but Inspector Zhang stopped her with a wave of her hand.

'The clothing first,' he said. 'Do you notice anything?'

'A dress. Shoes. Bra. Pants.' Sergeant Lee shrugged. 'Nothing out of the ordinary.'

Inspector Zhang smiled. 'The dress is Karen Millen, is it not?'

Sergeant Lee examined the label. 'It is,' she said. 'You have a good eye for fashion, inspector.'

'Karen Millen is one of my wife’s favourite labels. Though she usually only shops there during the sales. It is an expensive brand.'

'I like Karen Millen myself, but you are right, they are expensive.'

'And the underwear,' said Inspector Zhang. 'I am less of an expert on underwear, but it also looks expensive.'

Sergeant Lee examined the bra and pants. 'Yes, it is of good quality,' she said. 'Real silk.'

Inspector Zhang nodded. 'Do you think they are the sort of items that would be purchased by a woman who lived in an HDB block?'

'Possibly not,' said Sergeant Lee.

'But the shoes, what about the shoes?'

Sergeant Lee picked up one of the shoes. 'Poor quality,' she said. 'Probably made in China.'

'And the bag. A Louis Vuitton copy. I thought that strange, that she was happy to pay for a Karen Millen dress but then had a fake handbag. And her shoes were not of good quality. The shoes and the bag fitted with the HDB apartment, but not the Karen Millen dress.

'And the underwear,' said Sergeant Lee.

'I wasn’t aware of the underwear at the time,' said Inspector Zhang. He gestured at the handbag. 'Let’s see

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