After dismissing a false confession by truffle scion Pietro De Rosa the previous day, who claimed to have stabbed mayor Dino Lombardi with his truffle knife, next on Antonio Rosetti’s list of potential suspects was the local olive oil producer Mario Pellegrino. The high-quality oil was with the truffles and local wine, one of the town’s three pillars of wealth and the vile Signor Lombardi had imposed harsh taxes on sellers and buyers after threatening his way to power in the picturesque southern Italian town of Cortoglia.

Antonio left the police station just after breakfast and set out for the olive oil shop in the town square, pleased he would have to pass the pharmacy on his way having been taken by the young woman who ran it the previous afternoon.

He slowed down as he approached the shop and glanced through the window. She was standing by the door, turning the closed sign to open, and looked up as he passed by. They exchanged a glance before he hurried on. When Antonio arrived at the olive oil shop, Mario Pellegrino was waiting for him at the door, having just placed a giant festive wreath made from olive branches and glittering stars in the window.

“Good morning, Lieutenant,” he said. “Have you come to purchase a bottle of the finest olive oil or is this a police raid?”

“I’m sorry I didn’t call and make an appointment, Signor Pellegrino, but…” Antonio said as he followed him into the shop. “You were hoping to take me by surprise,” said Pellegrino. “But I have to tell you, Lieutenant, I am not at all surprised.”

“You were expecting me?” said Antonio as he stood beside the counter and took out his notepad and pen.

“Yes, everyone knows you’ve been sent from Naples to investigate the death of Lombardi, and I assumed I would be among the first people you would want to question.”

“It’s no secret that I detested the man. So if you were going to arrest me, the last thing you’d do is to call up and make an appointment, because that would give me enough time to escape.”

Antonio put down his pen.

“But why would you want to escape, Signor Pellegrino?”

“Because everyone knows I murdered Lombardi, and I realised that it wouldn’t take too long for a smart young detective like you to work out who the killer was.”

“But why would you want to kill the mayor?’ asked Antonio.

“He was ruining my business with his protection racket and added taxes. And if that wasn’t enough, he was demanding kickbacks from my buyers, some of whom began to avoid the journey to Cortoglia as they feared they might be next. Another year and I would have had nothing to leave the children.”

Pellegrino stood up and stretched his arms across the counter as if expecting to be handcuffed.

“Before I arrest you, Signor Pellegrino,” said the policeman, “I will need to know how you killed the mayor.” Pellegrino didn’t hesitate. “I strangled the damn man,” he said.

“Just one minor problem,” Antonio replied. “I’m afraid Lombardi wasn’t strangled by you, or anyone else for that matter.’

“What a pity. But as I would have liked to have strangled the man, can’t you just charge me with attempted murder, and that will solve all our problems?”

“Except for the problem that the culprit will still be on the loose,” said Antonio. “So if you’d be kind enough to advise your friends that I intend to catch the real murderer and put him behind bars, I’d be very grateful.” “I wonder if I might ask you for a small favour,” Pellegrino said. “I just wondered if you could let me know how the mayor was killed.”

The young policeman ignored the request and left the shop.

Antonio was on his way back to the police station to write up another abortive report but hesitated when he reached the pharmacy. He entered and found the young chemist, who he had deduced was Francesca Farinelli, daughter of Lorenz Farinelli, standing behind the tinsel-bedecked counter, chatting with a customer.

“That should ease the pain, signora, but make sure that you only take one pill a day before going to bed. And if it doesn’t get any better, come back and see me,” she said. Francesca turned to face Antonio. “Is it my turn to be arrested, Lieutenant?”

“No, something far simpler than that. I’ve run out of toothpaste.”

“You know, we do have customers who buy soap, toothpaste and razor blades all at the same time, or is this nothing more than subtle police tactics to wear the suspect down and make her admit she killed the mayor?” Antonio laughed. “However,” Francesca continued, “if your plan was simply to ask me out for a drink after I get off work this evening, I might just say yes.”

“Was it that obvious?”Antonio asked.

“Why don’t we meet at Lucio’s around six?” “I’ll look forward to it,” said Antonio as he turned to leave.

“Don’t forget your toothpaste, Lieutenant.”

When Antonio returned to the police station, there was a large, burly man wearing a long white coat and a blue and white striped apron waiting for him outside the front door. “Good morning, Inspector. My name is Umberto Cattaneo.”

“Lieutenant, Signor Cattaneo,” corrected Antonio.

“I feel confident, Lieutenant, that promotion will not be far away when you hear what I have to tell you.”

“Please don’t tell me you killed the mayor?”

“Certainly not,” said the butcher as he lowered his voice. “However, I can tell you who did kill Lombardi.”

At last, an informer, thought Antonio. He unlocked the door to the station and led Cattaneo through to his little office.

“But before I let you know who the murderer is,” continued Cattaneo as he sat down, “I need to be sure that it won’t be traced back to me.”

“You have my word on that,” said Antonio, opening his notepad. “That’s assuming we won’t need you to act as a witness when the case comes to trial.”

“You won’t need a witness,” said Cattaneo, “because I can tell you where the gun is buried.”

Antonio snapped his notepad shut, and let out a deep sigh.

“But I haven’t even told you who the murderer is,” Cattaneo protested.

“You needn’t bother, Signor Cattaneo, because Lombardi wasn’t shot.”

“But Gian Lucio told me he’d shot him. He even showed me the weapon,” insisted Cattaneo.

“Before I lock you both up for a couple of days, if for no other reason than to stop any more of you wasting my time, may I ask why are you so willing to get your friend arrested for a crime I can assure you he didn’t commit?”

“Gian Lucio Altana is my oldest and dearest friend,” protested the butcher.

“Then why accuse him of murder?”

“Because I lost the toss,” said Cattaneo. “You lost the toss?” “Yes, we agreed that whoever won would give himself up and admit that he’d killed the mayor.”

“Then why hasn’t he given himself up?” said Antonio, unable to hide his frustration.

“Signor De Rosa advised us against that. Said there had been far too many confessions already, and he felt Gian Lucio would have a better chance of being arrested if you thought I was an informer.”

“May I ask why Gian Lucio was so willing to be charged with a murder that he didn’t commit?’

“Oh, that’s easy to explain, Lieutenant. Lombardi used to eat at Gian Lucio’s restaurant three times a day and he never once paid the bill.”

“That’s hardly a good enough reason to kill someone.”

“It is when you lose all your regular customers because none of them want to eat in the same restaurant as the mayor. By the way, Lieutenant, was Lombardi electrocuted by any chance?”Get out of here, Signor Cattaneo, before I get myself arrested for murder.”

Not a totally wasted morning, considered Antonio, because he was now confident only he, Constable Gentile and the murderer had any idea how Lombardi had been killed. But where was Gentile?

Antonio arrived at Lucio’s restaurant just before 6pm, looking forward to seeing Francesca. He sat at an outside table and placed a bunch of flowers on the chair next to him, smiling when the owner Gian Lucio joined him.

“Can I get you a drink, Lieutenant?”

“No, thank you. I’ll wait until my guest arrives. And Gian Lucio,” Antonio said as the restaurateur turned to leave, “just to let you know your friend Signor Cattaneo tried to get you arrested for murder this morning.”

“‘I know, but then I did win the toss,” sighed Gian Lucio.

Antonio continued to look across the square to the pharmacy until he spotted Francesca locking up. He watched her crossing the square and immediately realised it was the first time he’d seen her not wearing a long white coat. She was dressed in a red silk blouse, a black skirt and a pair of high-heeled shoes that certainly hadn’t been bought in Cortoglia.

He tried not to stare at her. What else was different? Of course, she’d let her hair down. He hadn’t thought it possible that she could be even more beautiful.

“As you’re a highly trained detective,” Francesca said when she sat down next to him, “you will know that my name is Francesca, while I’m not sure if you are Antonio or Toni?”

“My mother calls me Antonio, but my friends call me Toni.”

“Does your family also come from Naples?”

“Yes,” said Antonio. “My parents are both schoolteachers.”

Francesca laughed. “Any brothers or sisters?”

“Just one brother, Darius. He’s a lawyer. So once I’ve locked any criminals up, he puts on a long black gown and defends them. That way we keep it all in the family.”

Francesca laughed again. “Did you always want to be a policeman?” she asked, as Gian Lucio handed them both a glass of wine.

“From the age of six when someone stole my sweets. But to be fair, if you’re brought up in Naples, you have to decide early which side of the law you’re going to be on. Did you always want to be a pharmacist?”

“I first worked in the shop at the age of 12,” she said, looking across the square, “and with the exception of four years at Milan University studying chemistry, it’s been my second home. So when the owner retired, I took over.”

She paused: “How many people admitted to killing the mayor today?”

“Only one. The florist, Signor Burgoni.”

“So how did he bump off Lombardi?” Francesca asked.

“Claimed he ran him down in his Ferrari, and then reversed over him to make sure he was dead. Right here in the town square.”

“Sounds pretty convincing to me, so why didn’t you arrest him?”

“Because he doesn’t own a Fiat, let alone a Ferrari, and what’s more, doesn’t even have a driving licence,” said Antonio, as he handed Francesca the flowers.

“So he’ll be able to continue selling his flowers.”

The couple stood up and began to walk across the square towards the pharmacy where Francesca had an apartment above the shop.

“It won’t be long before I have to return to my little flat in Naples,” sighed Antonio.

“Not if you don’t catch the killer,” she teased. When they reached Francesca’s door, she took out a key.

But before she could put it in the lock Antonio bent down and kissed her.

She smiled: “I look forward to seeing you tomorrow.”

Antonio looked puzzled until Francesca added: “I have a feeling that it can’t be too long before you’ll need another bar of soap. By the way, Toni, some of our customers buy them in boxes of three, even six.”

• Exclusively adapted by Jeffrey Archer for the Daily Express from Who Killed The Mayor. His latest must-read thriller, Next In Line (HarperCollins, £22), featuring William Warwick, is out now. Lord Archer’s fee has been donated to Give A Book.