In addition to the 58 people who died, nearly 500 were injured.

“We still do not have a clear motive or reason,” a frustrated Clark County Undersheriff Kevin McMahill said on Friday. “We have looked at literally everything.”

Investigators have chased 1,000 leads and examined Stephen Paddock’s politics, his finances, any possible radicalisation and his social behaviour – typical investigative avenues that have helped uncover the motive in past shootings.

“We have been down each and every one of these paths,” McMahill said. “We all want answers.”

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

McMahill said investigators had reviewed video from the casino and don’t think Paddock had an accomplice, but they want to know if anyone knew about his plot beforehand.

Investigators have been looking into whether he was with a prostitute days before the shooting, were scrutinising cruises he took and were trying to make sense of a cryptic note with numbers jotted on it found in his hotel room, a federal official said on condition of anonymity.

“We’re so used to ... 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,” said Erroll Southers, director of home-grown violent extremism studies at the University of Southern California.

Paddock’s girlfriend, Marilou Danley, told FBI agents on Wednesday that she had not noticed any changes in his mental state or seen indications he could become violent, according to another federal official on condition of anonymity.

Because so few people knew Paddock well, investigators will have a harder time probing his background for clues, Southers said.

There’s “no one to say who’s he mad at, what his motive is,” Southers said. “The key to this case right now is the girlfriend.”

Associated Press, Reuters