(CNN) -- The one question we all desperately want answered may have gone to the grave with Aaron Alexis: Why?

Why did he park at the Washington Navy Yard on Monday, walk into Building 197, perch himself on an overlook above the atrium and open fire? The bullets that rained down killed 12 people and wounded eight others.

Why?

But that's not the only missing puzzle piece. Investigators are painstakingly trying to piece together the motive, the means and the method.

"No piece of information is too small," Valerie Parlave of the FBI said Monday night. "We are looking to learn everything we can about his recent movements, his contacts and associates."

For now, here's what we know and what we don't know.

THE DEATH

What we know: The shooting rampage ended with the death of Alexis, 34.

What we don't know: How Alexis died. Authorities say he was killed after an encounter with security. We've yet to learn the details.

THE MOTIVE

What we know: Senate Majority Leader Harry Reid may have said it best Tuesday when he told colleagues that "there is no explanation for the violence." So far, investigators haven't offered any clue as to what motivated Alexis to kill. Friends say he had been frustrated over pay and benefits issues from a previous contracting job, and federal law enforcement sources said he may have contacted Veterans Administration hospitals for possible treatment of psychological issues. But so far, investigators haven't said if either of those issues contributed to the attack.

What we don't know: What he might have left behind in his Washington hotel room, either in writing or on any computers FBI agents may have found while searching the room.

A SECOND MAN?

What we know: Throughout the day, authorities said they were looking for a second man. But by nightfall, they said they were "confident" that Alexis was the lone gunman. "We have exhausted all means to eliminate that possible last suspect," said Metropolitan Police Chief Cathy Lanier. "So we do now feel comfortable that we have the single and sole person responsible for the loss of life inside of the base."

What we don't know: At the same news conference, just a few minutes before Lanier spoke, Washington Mayor Vincent Gray muddied the picture. "We continue to pursue the possibility of there being another shooter," he said. "We don't have any evidence, any indication at this stage that there was another shooter, even though we haven't completely ruled that out."

THE VICTIMS

What we know: We now have all the names of the victims. They range in age from 46 to 73. Three others were shot, but survived and are doing better at a Washington hospital, doctors said Tuesday. Five more suffered contusions and chest pains, the mayor said.

What we don't know: We have yet to find out more about the victims, such as what they did at the Navy Yard, where they were at the time of the shooting, etc.

HIS HISTORY

What we know: He was an IT contractor. He had medium security clearance, high enough to work at multiple Navy offices over the summer. He had an ID badge to enter the Navy Yard. His employer says the shooter jumped through all the right hoops. "Alexis had a security clearance that was updated in July, approved by military security service personnel," said Thomas Hoshko, CEO at The Experts. "There is nothing that came up in all the searches." We've also learned more about his military record. Navy officials moved to discharge him in 2010 over a pattern of misconduct that included insubordination, unauthorized absences and other infractions, according to a U.S. defense official. It wasn't enough for a general discharge, so Navy officials decided to grant him an honorable discharge, the official said.

What we don't know: How he was able to get a security clearance with such a spotty background. Former Navy SEAL Cade Courtley says a poor or incomplete background check is to blame. "Most people, when they get into that, they are given an interim clearance, and that means that the background check hasn't been done but it's in the process of being done," Courtley said. "He may have started out with an interim clearance and a background check should have been done." The former SEAL says just running Alexis' fingerprints would have turned up his arrest record. In Seattle, he fired several shots into the tires of a car during an altercation over construction near where he lived in 2004. There was also a weapons incident in Texas in 2010.

SECURITY AT THE YARD

What we know: Alexis drove onto the grounds of Navy Yard on Monday morning with three weapons in his vehicle. He took the weapons out, proceeded into Building 197 and opened fire. He had access to the Navy Yard because of his contracting work, and he used a valid pass to gain entry.

What we don't know: Even to drive or walk onto the base, a person would be required to present credentials, said Navy Capt. Mark Vandroff. Building 197 has armed security at the door. How did he get the guns past them? Did cost-cutting compromise Navy security? Rep. Mike Turner, an Ohio Republican and a member of the Armed Forces Committee, thinks so. He wants a congressional briefing from the Pentagon inspector general on a Navy security audit that he says was released after Monday's shooting. "It is my understanding that the IG report indicates the Navy may have implemented an unproven system in order to cut costs," Turner said. "I also learned that potentially numerous felons may have been able to gain restricted access to several military installations across the country due to insufficient background checks, increasing the risk to our military personnel and civilian employees."

HIS WEAPONS

What we know: Federal law enforcement sources say authorities have recovered three weapons from the scene of the mass shooting, including one -- a shotgun -- that investigators believe he brought in to the compound. The other two weapons -- handguns -- the sources say, may have been taken from guards.

What we don't know: The sources, who have detailed knowledge of the investigation, cautioned that initial investigation information that an AR-15 rifle was used may have been incorrect. It is believed that Alexis had rented an AR-15, but returned it before Monday morning's shootings. Authorities are still investigating precisely how many weapons Alexis had access to and when.

GUN DEBATE

What we know: The incident will certainly rev up the often explosive debate over gun control. But initial reports show Alexis obtained his primary weapon legally.

What we don't know: Will the shooting at Navy Yard change the political landscape? High-profile shootings over the last several years have done little to move the needle in Washington. President Obama pushed for universal background checks and other directives after the the Newtown, Connecticut, shootings, to cut down on the access Americans would have to firearms, but they never gained traction. At the state level, it's been a similar story. The successful recall elections last week of two Colorado lawmakers who backed new gun restrictions sent a shiver through the gun control lobby.