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‘Did she talk to you about her life?’

‘That night?’

‘Any night.’

‘She liked Bath, she say. Plenty good ladies’ shops. Azzuro, Annabel Harrison, Kimberly. All her money go on nice Italian clothes. I have a joke with her that she serve Italian so she can buy Italian.’

‘Did she mention her two daughters?’

‘To me? No. Luigi tell me she have daughters.’

‘How about you, Carlo? Are you married?’

‘Am I married?’ He stopped chopping and drew the knife across the front of his throat, rolling his eyes. ‘Three times. Five kids. Four back in Napoli with wives one and two, must have cash every month. One baby son here. And wife number three.’

‘Here in the city?’

‘No chance. I keep her away from those dress shops. Combe Down.’

‘Do you drive?’

‘Can’t afford. I take the bus.’

Diamond asked to see the locker room. It was through the kitchen and Tosi the owner took this as his chance to grab the limelight again. He wanted it known that his facilities met the hygiene regulations and insisted on showing the staff toilet and washroom as well. Luigi’s description of the locker room was right. It was little more than a cupboard with three metal lockers and barely space to change your clothes. When Diamond had established which locker was Delia’s, he asked Halliwell to go in and force the lock.

‘No, no,’ Tosi said in alarm. ‘No damage please. I have extra key.’

He went away to fetch it.

Halliwell leaned against the locker door and it opened. ‘Not much of a lock,’ he said.

The faint smell of scent carried to them, as if Delia herself was protesting that her privacy was being invaded again. Diamond took Halliwell’s place in the small space. He found a hanger with two white blouses and a black skirt. On the shelf above were two bars of KitKat, a box of tissues, a mirror, a lipstick and a comb.

Tosi returned with the key. ‘So I waste my time, eh? Open after all?’

Ignoring him, Diamond stooped to pick up a pair of low-heeled black shoes. Under them was a book of matches. ‘Was she a smoker?’

‘No smoking, no.’

‘Are you sure?’

‘Nobody here smokes,’ Luigi said.

So why did she want matches? Diamond returned the shoes to the locker, picked up the matches and folded back the flap. None had been used. They were black, with white tips, from the Hilton Hotel, Bath. Someone had written the number 317 under the flap. He slipped them into his pocket.

On the way out, he stopped to look at Luigi’s bike, chained to a post in the space under the stairs. ‘I should get one of these,’ he said to Halliwell without meaning it. ‘Give me six months and I’d be as slim as that waiter.’

‘It’s the job that keeps him in shape,’ Halliwell said.

‘What are you saying — that I should get off my butt more often?’

‘I was talking about the waiter, guv.’

Towards the bottom of Milsom Street, outside Waterstone’s bookshop, Diamond stopped walking again, causing Halliwell real concern about his health. The short distance they’d covered had been all downhill. ‘We’ll go in here,’ the big man said.

‘Are you after a book, guv?’ Halliwell said, playing along with him.

‘They have a coffee shop up here,’ he said, surprising Halliwell by climbing the stairs two at a time. At the top he was still breathing normally. ‘I was counting on Tosi offering us one. He missed an opportunity of cosying up to us there. Not so much as a complimentary peppermint on the way out.’ He looked over the display of pastries. ‘We’ll go halves on one of those almond croissants, right?’

Halliwell, who never took snacks, didn’t like to disappoint him.

At a table by the window they shared their findings. Luigi the waiter had to be a prime suspect. He’d been the only man in the restaurant at the end of the evening, the last known person to have seen Delia alive. Never mind his insistence that he’d used a bike that evening. He owned a car and he could have parked it nearby and offered her a lift and driven her to his home for a night of passion.

‘Two nights,’ Diamond said, recalling that she wasn’t found until Thursday. ‘That’s a lot of passion.’

‘Maybe he was keeping her there against her will,’ Halliwell said. ‘Most Italian guys think they’re God’s gift to women.’

‘And finally killed her when it didn’t work out the way he wanted?’

As for the others in the restaurant, Diamond said, he didn’t rate them as suspects. He couldn’t see the pot-bellied Signor Tosi suspending a body from a swing. It would require considerable strength. Neither could he picture Carlo as the killer. The way the little cook had talked of having three wives — rather than two ex-wives — suggested he collected women rather than disposing of them.

‘There’s the lone diner as well,’ Halliwell said.

‘Mr D. Monnington. Decent of Luigi to go to all the trouble of getting the name for us,’ Diamond said with irony.

‘You think he’s keen to swing it on someone else?’

‘That was my reading.’

‘Monnington’s top of my list,’ Halliwell said. ‘I can see it happening: the businessman stuck in a hotel, looking for amusement. Goes for a meal, picks up a waitress, invites her back. Likes her enough to spend the next day with her. Something goes wrong between them and he gets in a strop, strangles her and hopes to fake the suicide and get away with it.’

‘Put like that, it’s possible. Have him checked out when we get back, Keith.’

‘How do you mean? See if he’s got form?’

‘And check the hotels.’ Diamond muttered something under his breath as another thought struck him. ‘But would a stranger to the town know where to string up the body?’

‘Maybe they took an evening walk in the park and he saw the swings and took his opportunity.’

‘With a length of plastic cord someone had conveniently left?’ Diamond said, sitting back and shaking his head. ‘I don’t think this was dreamed up at the scene, Keith. The killer planned it.’

‘And you’re backing Luigi?’

‘I’m saying he’s got to be taken seriously, along with the missing father of her children, Danny. And of course Ashley, the laid-back musician.’ He looked across at the rest of the almond croissant sitting on Halliwell’s plate. ‘Aren’t you going to eat your half?’

Out in the street again, he put his hand in his pocket and felt the hard edge of the book of matches. ‘Let’s cut through Shires Yard. I wouldn’t mind visiting the Hilton.’

The curious thing about working in a city is that you don’t get to see the hotels that visitors regard as a major part of the experience. Diamond wasn’t all that familiar with the Hilton. Built as the Beaumont Hotel in 1973, a low point in Bath’s architectural history, its blocklike exterior, with yellow stone cladding pretending to be the real local stone, led locals to describe it as a giant hunk of cheese.

To be fair, the management had done much to upgrade the interior. And Jenny the receptionist proved to be a star. ‘Does this count as helping you with your inquiries?’ she asked Diamond after he’d shown her his warrant card.

‘You’ll really help my inquiries if you can solve this puzzle,’ he said, handing her the book of matches. ‘It’s one of yours, right?’

‘Yes, they’re complimentary in the bar. What’s the puzzle?’

He asked her to open it.

‘Is it a trick?’ she said, as she unfastened it. Then she saw the number and smiled. ‘A room number?’

‘That’s what I was thinking,’ he said. ‘Do you have a 317?’

‘We do indeed.’

‘And would your computer tell us who has been staying in there over the last few days? It could be important,’ he added.

She got them a printout.

There were five names. The fourth was Dalton Monnington.

Diamond exchanged a look with Halliwell.

‘Would you have this one’s address?’