Lindsay, aged 13, bought cornflakes from a late store in Hebden Bridge, West Yorkshire, at 10.22pm on 7 November. She has not been seen since.
The police did not hesitate to launch what has been in scale, but not name, a murder inquiry. Divers have been in the river Calder and the Rochdale Canal.
Mountain rescue teams and mounted police have roamed the moors and woods, and nobody in Hebden Bridge or any of the other small valley communities can have failed to have seen her picture smiling from dozens of posters.
Five weeks later, the police do not even know whether Lindsay turned left or right as she left the Spar store on Crown Street.
Her parents, Geraldine and Gordon, are distraught, aware that the immediate local reaction to their daughter's disappearance contained muttered disapproval of their conduct as parents.
Lindsay was not reported missing until the morning, when the newsagent telephoned to find out why she had not arrived for her paper round. Her bed had been empty late the night before. Good parents, the whisperers said, would have noticed, and done something promptly.
The Rimers belong to that part of Hebden Bridge's population variously described as "hippy" or "very alternative". The town is not a divided community, or an intolerant one.
But in the aftermath of a dramatic and probably tragic event, some more conventional households could derive comfort from thinking that in some small measure the Rimers had been less vigilant than they could have been. The feeling intensified when Mr Rimer appeared at a police press conference.
He appealed to the publicfor help finding his daughter, but his demeanour appeared less than distraught.
"We had a few phone calls saying it was Dad who was responsible," Detective Superintendent Tony Whittle, leading the investigation, said.
"His manner and his facial expressions seemed unusual."
It is believed that Mr Rimer bitterly regrets that public appearance; Mrs Rimer was physically unable to appear.
Police believe the impression gained from television coverage of Mr Rimer's appearance reminded some viewers of recent homicide cases - two In West Yorkshire - in which the man making an emotional appeal was subsequently charged.
The police have no sympathy with the rumours. If Lindsay was abducted, no family in the valley can feel immune to the implications. Det Supt Whittle is known to have called the press conference reluctantly, persuaded only by the urgent need for public help in the absence of any hint of evidence about Lindsay's disappearance.
Hebden Bridge's "alternative" community may festoon its windows with stickers advocating the legalisation of cannabis but detectives speak warmly of the Rimer family and their friends.
"It is a community with a different lifestyle, but they have been at least as helpful as any other," Det Supt Whittle said. "There is a hippy commune there with plenty of pony tails, but there is no crime rate to speak of, and it is more of a community than a commuter estate."
Friends of the Rimer family organised a search of moorland by more than 100 volunteers last week. They will write this week to more than 6,000 local residents and businesses, asking for all empty property to be searched.
The Find Lindsay Rimer Appeal has asked for donations to be sent to the local branch of the Yorkshire Bank and the police have paid tribute to the positive local response.
The focus of the police investigation remains a bearded white man, aged in his forties or fifties, "approaching youngsters with undue interest" before and after Lindsay disappeared. He is believed to have driven a red Honda car, registration number FYY 215W, stolen in Leeds and later abandoned in Sheffield. There was no forensic evidence in the car which suggested that Lindsay had been a passenger.
The man's description bears resemblance to a man who disappeared abruptly from a Sheffield hotel.
The police, who have maintained a squad of about 50 officers on the inquiry, can be contacted on (0422) 337021.Reuse content