They have seen him smiling on a hostel security camera, but don’t know his name. They found the backpack he discarded while fleeing, but don’t know where he’s gone.

As the search for UnitedHealthcare CEO Brian Thompson’s killer goes on, investigators are reckoning with a tantalizing dichotomy: They have troves of evidence, but the shooter remains an enigma.

Police don’t know who he is, where he is, or why he did it, though they are confident it was a targeted attack instead of a random act.

“The net is tightening,” New York City Mayor Eric Adams said Saturday.

Hours after he spoke, police divers were seen searching a pond in Central Park, where the killer fled after the shooting. Officers have been scouring the park for days for any possible clues and found his bag there Friday.

Late Saturday, police released two additional photos of the suspected shooter that appeared to be from a camera mounted inside a taxi. The first shows him outside the vehicle and the second shows him looking through the partition between the back seat and the front of the cab. In both, his face is partially obscured by a blue, medical-style mask.

Retracing the gunman’s steps using surveillance video, police say, it appears he left the city by bus soon after the shooting Wednesday morning outside the New York Hilton Midtown. He was seen on video at an uptown bus station about 45 minutes later, NYPD Chief of Detectives Joseph Kenny said.

With the high-profile search expanding across state lines, the FBI announced late Friday that it was offering a $50,000 reward for information leading to an arrest and conviction, adding to a reward of up to $10,000 that the NYPD has offered. Police say they believe the suspect acted alone.

Police provided no updates on the hunt Saturday, but investigators are urging patience — even with a killer on the loose. Hundreds of detectives are combing through video recordings and social media, vetting tips from the public and interviewing people who might have information, including Thompson’s family and coworkers and the shooter’s randomly assigned roommates at the Manhattan hostel where he stayed.

“This isn’t ‘Blue Bloods.’ We’re not going to solve this in 60 minutes,” Kenny told reporters Friday. “We’re painstakingly going through every bit of evidence that we can come across.”

The shooter paid cash at the hostel, presented what police believe was a fake ID and is believed to have paid cash for taxi rides and other transactions. He didn’t speak to others at the hostel and almost always kept his face covered with a mask, only lowering it while eating.

But investigators caught a break when they came across security camera images of an unguarded moment in which he briefly showed his face soon after arriving in New York on Nov. 24.

Police distributed the images to news outlets and on social media but so far haven’t been able to ID him using facial recognition — possibly because of the angle of the images or limitations on how the NYPD is allowed to use that technology, Kenny said. On Friday evening, investigators found a backpack in Central Park that had been worn by the gunman, police said. They didn’t immediately reveal what, if anything, it contained but said it would be tested and analyzed.

Another potential clue, a fingerprint on an item he purchased at a Starbucks minutes before the shooting, has so far proven useless for identifying him, Kenny said.

Aided by surveillance cameras on nearly every building and block, police have been able to retrace the shooter’s movements.

They know he ambushed Thompson at 6:44 a.m. as the executive arrived at the Hilton for his company’s annual investor conference, using a 9 mm pistol that resembled the guns farmers use to put down animals without causing a loud noise. They know ammunition found near Thompson’s body bore the words “delay,” “deny” and “depose,” mimicking a phrase used by insurance industry critics.

Kenny said the fact that the shooter knew UnitedHealthcare group was holding a conference at the hotel and what route Thompson might take to get there suggested that he could possibly be a disgruntled employee or client.