About 8pm on the evening of May 3, 2007, Jenny Murat, a British expatriate living in the coastal village of Praia da Luz on Portugal's Algarve, notices a woman staring intently at an apartment block next to the Ocean Club, a small holiday complex popular with British families.
"I saw the woman standing on the corner of the street," Mrs Murat later recalled. "She caught my eye because she was dressed in purple-plum clothes. It struck me as strange.
"It's so usual for anyone, particularly a woman, to be standing alone on the street in our resort, just watching a building."
Sometime during the next two hours, three-year-old Madeleine McCann disappears from an apartment in that same block as her parents dine with friends nearby, said the Daily Mail.
"The next morning, we heard that a little girl had gone missing, and I later told police about the woman I'd seen right outside," Mrs Murat continued. "I didn't recognise her and don't have a clue who she is, but she seems a bit suspicious.'
It is this "woman in purple", the Mail understands, who is keeping alive Operation Grange, the marathon reinvestigation of the Madeleine McCann case by Scotland Yard, now in its sixth year.
The suspect is believed to be Bulgarian and was living in Praia da Luz with her partner, a man of German or Eastern European descent (now believed to be dead) at the time of Madeleine's disappearance. It is thought that police interest is linked to discoveries about her late partner's history.
In the past few months, the Grange team - now down to four detectives from a peak of 31 - has been criss-crossing Europe trying to locate the woman.
Their budget had been due to run out in September, but officers are understood to have used the 'woman in purple' line of investigation to persuade the Home Office - which is financing the inquiry from central government funds - to grant a six-month extension.
The $291,500 agreed will allow inquiries to continue until March, taking the total spent on Operation Grange near to $23 million.
Given that Mrs Murat (whose son Robert was arrested as a suspect two weeks after Madeleine's disappearance, but cleared of any involvement) raised the alarm about the woman on the morning after the alleged abduction, it must be asked why it has taken ten years for attention to focus on this suspect? Equally pertinent, perhaps, is the question: why is the British taxpayer being asked to finance Operation Grange further when all other leads have come to dispiriting dead-ends?
During the past six years, a string of theories and suspects have come and gone.
Variously, the spotlight has fallen on a group of British contract cleaners working in the resort, a smelly, pot-bellied man, a burglary gang posing as charity collectors, child-traffickers, gypsies and so on.
Of course, it must be acknowledged that the suffering of Madeleine's parents, Gerry and Kate McCann, over their daughter's disappearance is as unimaginable as it is unending.
Every parent will sympathise with their conviction that, until proven otherwise, Madeleine may yet be found alive and well.
But the brutal and tragic truth is that it is more than probable the woman in purple is unlikely to be the key to solving this mystery.
Operation Grange has been one of the longest, most high-profile and costly police investigations in history. Launched in May 2011, officers have sifted (and translated) 40,000 documents produced by Portuguese police who conducted the initial investigation, and by the eight teams of private detectives who have worked on the case.
Some 600 'persons of interest' have been examined and 'sightings' of Madeleine - in Brazil, India, Morocco and Paraguay, on a German plane and in a New Zealand supermarket - assessed.
The demand from many quarters - from the McCanns, from the public, from politicians - for the investigation to continue is, of course, entirely understandable.
But there comes a time in every police inquiry into a disappearance when the question of how long it should continue has to be asked.
In an era of austerity - with the Met threatening to stop investigating thousands of "low-level" crimes, such as burglaries and assaults, to help it absorb £400 million in cuts before 2020 - the commitment to one increasingly old, and cold, case is becoming harder to defend.
Some police critics of Operation Grange point to what they see as its "original sin" - the failure of the Met's team to re-interview Gerry and Kate McCann and the so-called Tapas Seven, the friends with whom they were dining in a restaurant at the Ocean Club on the night of Madeleine's disappearance.
This, it is argued, should have been a basic first step in a reinvestigation while implying no guilt on the part of those involved.
According to Mark Rowley, Assistant Commissioner of the Met, there was simply no need to re-interview the group because local police had already done so. Yet the initial inquiry by police on the Algarve is known to have been deeply flawed.
Might not a British interviewer of the McCanns and their friends have picked up on something not spotted by the Portuguese?
Speaking shortly before the tenth anniversary of Madeleine's disappearance, Mr Rowley explained: "We had a look at all the material and we are happy that was all dealt with, and there is no reason whatsoever to reopen that or start rumours that that was a line of investigation."
According to a friend of the McCanns, "it would have been hugely insulting to Kate and Gerry if their original statements had been questioned. There was no need to say anything more because everything had been said".
What this meant in practice was that abduction, either by design or as the result of a break-in gone wrong, was the only consideration for the Grange team.
The reinvestigation began after the McCanns found a powerful ally in the shape of Rebekah Brooks, then chief executive of News International (publisher of The Times, Sunday Times and The Sun), who was anxious to secure the newspaper publishing rights for Kate McCann's book on the family's terrible ordeal.
Ms Brooks was subsequently accused during the Leveson Inquiry into Press standards of bullying the Prime Minister David Cameron and Theresa May, then Home Secretary, into initiating Grange.
She denied the accusation, but admitted applying pressure for a case review on the McCanns' behalf.
Politics has been a consideration in the conduct of Operation Grange ever since; certainly, it was the subject of discussions between David Cameron and his Portuguese opposite numbers.
One could argue that delaying the end of the inquiry postpones the moment when Mrs May, an increasingly embattled prime minister, must explain why so many millions and countless hours of police time -resources committed on her watch as Home Secretary and PM - have ended up in a fruitless dead-end.
Disquiet about Operation Grange is nothing new. In 2015, John Tully, then chairman of the Metropolitan Police Federation, argued that, in a time of cuts at home, Scotland Yard should not be used to conduct inquiries into matters abroad.
"It is surprising to see an inquiry like the McCann investigation ring-fenced,' he said. 'I have heard a few rumblings of discontent about it."
Colin Sutton, a retired senior detective at Scotland Yard, has told how he was warned off taking the leadership of Operation Grange.
A senior officer, who Sutton knew well, told him: "You wouldn't be happy leading an investigation where you were told what you could look at and what you could not."
Meaning, presumably, that the McCanns were off-limits to further questioning.
Mr Sutton recalls: "It was made clear that this was an unofficial call and that it was made in my interest - so that I might not end up taking on a task which would ultimately frustrate me.
"I do though think that a point worthy of reinforcing is that a proper, conclusive and reasoned elimination or implication of Kate and Gerry McCann would have been in everyone's interest, most of all theirs. That would have been my first objective had I been leading Operation Grange...To eliminate or implicate those closest to the child in this type of case is not only the documented best practice, but is common sense.
"Had Grange done this, then everything would be a lot clearer. I have no idea why this was not done, but I am satisfied [by] what has been said by the Met and what [information] is available that it was not [done]."
Following the departure in late 2014 of Andy Redwood, the officer originally in charge of the inquiry, Operation Grange has been the responsibility of Detective Chief Inspector Nicola Wall.
Taking on an investigation in its death throes must be something of a poisoned chalice, and DCI Wall may not be sorry to see the end of Grange in March 2018.
Meanwhile, the McCanns keep a close eye on developments from their home in Rothley, Leicestershire, and continue to express thanks to the Met.
"Kate and Gerry are grateful for the resources put into finding Madeleine and encouraged that they continue to be so," says the friend.
In Praia da Luz, however, locals are weary of the case, and the extension of Grange has been greeted with little enthusiasm.
According to Paul Luckman, of English-language newspaper The Portugal News: "There was this slightly arrogant British assumption that: "We'll come in and show you how to conduct an investigation". Well, we've seen the result.
"And the money. What about all the other missing children? There must be a limit to spending on a single case. The one consistent sentiment among [the] Portuguese, who are very family-focused, is to ask why Madeleine and her siblings were ever left alone in the first place. Parents here would take their children with them to the restaurant."
In a symbol of solidarity with the McCanns, De Lisle College in Loughborough - the secondary school Madeleine, who would now be 14, would have attended - continues to reserve a place for her. This year, she would have started her GCSE course.
Unless the woman in purple is tracked down in the next few months, the moment of closure for Operation Grange is approaching.
Despite a monumental effort, the case of Madeleine McCann, one of the most haunting mysteries of modern times, is likely to remain just that.