Police investigating the Las Vegas mass shooting have said they are still no closer to working out what drove Stephen Paddock to commit mass murder.

Paddock unleashed gunfire on Sunday from the 32nd floor of the Mandalay Bay hotel casino on the Las Vegas Strip, killing 58 and injuring nearly 500 people.

He killed himself as police closed in. Investigators – who have chased 1,000 leads – have announced plans to put up posters as they appeal for information.

Shooting timeline(PA graphics)

Undersheriff Kevin McMahill said: “We still do not have a clear motive or reason why. We have looked at literally everything.”

The FBI announced that billboards would go up around the city asking anyone with information to phone 800-CALL-FBI.

“If you know something, say something,” said Aaron Rouse, agent in charge of the Las Vegas FBI office. “We will not stop until we have the truth.”

Mr McMahill revealed at a news conference on Friday that police are confident there was not another gunman in Paddock’s room, and do not have any information that anyone else used his room key.

A memorial displaying 58 crosses near the Welcome To Las Vegas signA memorial displaying 58 crosses near the Welcome To Las Vegas sign (Mikayla Whitmore/Las Vegas Sun via AP)

Paddock, 64, fired indiscriminately from his upper-level room at the Mandalay Bay hotel casino at people attending a country music festival below.

Investigators believe Paddock hired a prostitute in the days leading up to the shooting and were interviewing other sex workers for information, an official briefed by federal law enforcement officials said.

The official also disclosed that Paddock took at least a dozen cruises abroad in the last few years, most of them with his girlfriend, Marilou Danley.

It is unusual to have so few hints of a motive five days after a mass shooting. In previous mass killings or terrorist attacks, killers left notes, social media postings and information on a computer – or even phoned police.

“The lack of a social media footprint is likely intentional,” said Erroll Southers, director of homegrown violent extremism studies at the University of Southern California.

Marilou DanleyStephen Paddock’s girlfriend Marilou Danley (Las Vegas Metropolitan Police Department via AP)

“We’re so used to, in the first 24 to 48 hours, being able to review social media posts. If they don’t leave us a note behind or a manifesto behind, and we’re not seeing that, that’s what’s making this longer.”

What officers have found is that Paddock planned his attack meticulously.

He requested an upper-floor room overlooking the festival, stockpiled 23 guns, a dozen of them modified to fire continuously like an automatic weapon, and set up cameras inside and outside his room to watch for approaching officers.

In a possible sign he was contemplating massacres at other sites, he also booked rooms overlooking the Lollapalooza festival in Chicago in August and the Life Is Beautiful show near the Vegas Strip in late September, according to authorities reconstructing his movements leading up to the deadliest mass shooting in modern US history.