(Credit: Frank Franklin II/AP Photo)

Hillary Clinton told "The Daily Show" host Jon Stewart that leaders face "hard choices" on the crisis in Israel and Gaza, giving a perhaps inadvertent plug for her memoir, while also telling him she likes to work out of her home and prefers an office with "fewer corners," when he plied her with questions about her potential presidential bid.

Stewart asked the former secretary of state about the current situation in the Middle East, noting her involvement in the previous 2012 crisis, and asked Clinton, "Can we at least agree the humanitarian crisis in Gaza is overwhelming and the world must do more for the people who are trapped by this conflict?"

"Yes," she said. "They are trapped by their leadership, unfortunately.

"It's a two-prong trapping. They have leadership that is committed to resistance and violence and therefore their actions are mostly about, 'How do we get new and better missiles to launch them at Israel?' Instead of saying, 'Hey, let's try to figure out how we are going to help make your lives better,'" Clinton told Stewart, referring to Hamas.

In a lengthy back-and-forth with Stewart she said Israel is "absolutely right" that it has to defend itself from Hamas rocket attacks, but expressed sympathy for the people of Gaza who she said are "trapped."

"They are trapped first and foremost by leadership that doesn't really want to make the situation too much better because that gives them a lot of leverage over the poor people in Gaza," she said, noting the current crisis is a "terrible dilemma."

"Unless we can give people enough of a sense of security on both sides that they will be better off and their children are going to be better off, then the guys with the guns can always disrupt anything," Clinton said.

"There are extremists on all sides and people with guns on all sides so leadership has to be very tough minded and very strong to make the hard choices," Clinton said, using the name of her memoir, a reference that Stewart immediately jumped on: "What? You did not do that? Wow."

The audience, as well as Clinton, burst into laughter.

Stewart opened up the show, before the interview, telling his audience Clinton would "publicly and "definitively" declare her candidacy, which drew huge applause from the crowd.

Almost immediately the 2016 talk started, even as Clinton began to discuss her memoir.

"I think I speak for everybody when I say nobody cares, they just want to know if you are running for president," Stewart deadpanned.

Clinton, wearing a black pant suit with gray polka dots, played along, telling Stewart she "was going to make an announcement," but his opener "spoiled it for me," adding "I think I'll just reconsider where I go do it."

Stewart said he "sensed confusion" from Clinton and told her he would give her a "career aptitude test," telling her it will help "hone in" on whether she even wants to be president.

The first question was whether Clinton likes "commuting to work" or if she prefers a "home office."

"I spent so many years commuting, I kind of prefer a home office," she quipped.

Stewart then asked if she has a "favorite shape" for that home office, asking if she would prefer it to have "corners or not to have corners?"

She answered since "the world is so complicated" she would prefer "fewer corners," to loud applause from the audience.

Stewart ended the bit by saying it sounded to him like she "declared for president."

The appearance was the third for Clinton on the show and Stewart noted the massive amount of press attention she gets, asking if she thinks it will stop if she decides against running. She answered, "I think a lot of people would lose their jobs if it stopped."

"I've been amazed at what a cottage industry it has become," Clinton answered, referring to not only press attention, but also two new unauthorized books that have been written about her.

The interview will air at 11 p.m. ET, but "The Daily Show" let in reporters to watch Clinton's interview during the earlier taping.