Detectives investigating the death of Mary Logie in Leven now strongly believe that she was murdered on the Tuesday morning.
They have also pledged that high visibility patrols will continue in the area for the foreseeable future.
The murder of Mary, known as Rae, shocked many within the community.
She was killed in her home in Green Gates, Leven, and detectives are now following a number of lines of enquiry.
In a updated briefing they said they ’’now strongly believe’’ the murder was committed some time on the morning of Tuesday, January 5.
Senior Investigating Officer, Detective Chief Inspector Keith Hardie of the Major Investigation Team, said: ‘‘She was last seen alive at 8am and so we are now focusing on the remainder of the morning.’’
He added: “We are working tirelessly to ensure every piece of evidence is gathered, all enquiries are carried out comprehensively and we can give Mary’s family, friends and the local community answers to why this terrible event has occurred.
“A great deal of activity has been taking place in and around Green Gates, and the ongoing assistance from the local community has been tremendous and vital in helping us develop our enquiries. I understand the concerns expressed by some local people and the media when they have asked for more explanation that we’ve been unable to give.
“Officers have spoken with various people in connection with this ongoing effort and we’re not at a stage where we can release much detail about the actions being carried out. We must always protect the integrity of the investigation and there is information, which has to be kept within the inquiry team.
“I want to give my personal assurance to the community that our investigation is thorough and officers are doing a tremendous amount of work to ensure Mary’s killer is brought to justice.”
A mobile incident vehicle is still outside her home to allow members of the public to speak to officers involved in the investigation.
Chief Inspector Adrian Annandale, the Local Area Commander for North East Fife, said: “High visibility patrols have been undertaken in the Green Gates area since the murder was reported to police and this will continue for the foreseeable future.
“A crime of this type is extremely rare for Fife and I understand that people may have concerns. However, we welcome the opportunity to engage directly with members of the public and we’re taking steps to do this whenever we can, working with our community partners to ensure that anyone who is worried knows where to turn.
“Please do come and talk to your local officers, at the mobile incident vehicle or out on the streets. I also urge anyone who has any information in relation to this murder to contact police on 101 or anonymously through the charity Crimestoppers on 0800 555 111.”