Toya Carmichael, Mary Dickson and Donna Campbell met last month at the Kennedy Center, where they waited for nine hours for tickets to this summer’s blockbuster, “Hamilton.” The group left empty-handed that day because only $600 tickets were left when they got to the box office window for the members-only sale.

But the wait wasn’t in vain, since the newfound friends hatched a plan to work together for Monday’s public sale.

“I’ve never done anything like this before,” Dickson said, the fur-edged hood of her red parka pulled down to her eyes. The friends agreed to tag-team the next sale, getting in line 24 hours before the box office opened Monday at 8 a.m. and taking shifts to keep their place.

As a result, the team was at the front of a line of several hundred people that snaked around the white marble walls of the Kennedy Center. Despite the cold, the plaza had a party atmosphere, with people in chairs and sleeping bags in a haphazard formation hundreds of yards long. One group played cards on a blanket spread on the stone deck. Others bought coffee and doughnuts that the Kennedy Center brought out just before dawn.

The Kennedy Center hosts Lin-Manuel Miranda’s hip-hop musical biography of the Founding Fathers for 14 weeks starting June 12. Tickets were priced at $99, $149, $179, $199 and $625, plus fees of 14 percent for phone and online purchases.

A members-only sale on Feb. 28 was marred by computer troubles and high demand that at one point topped 80,000 users online. The demand seemed equally high on Monday, but there were fewer reports of problems, which last month included changes in ticket prices and dates.

Monday’s public sale progressed more smoothly. Patrons appeared to be moving more quickly than it did for the Feb. 28 sale. By 3 p.m. – seven hours after signing on — users who had places 30,000 and higher were reporting purchases, and some were praising the arts center. Kennedy Center seemed to be responding more quickly to patron question and issues on Monday, too.

But it wasn’t perfect. Some patrons received an error message after submitting payment, an issue the Kennedy Center described on social media. If the order was in a patron’s account, the arts center will email in the next 24 hours, according to a social media post.

The Kennedy Center will not say how many members it has, but many came away without seats. Among them were Carmichael, Campbell and Dickson. Each had been members before the arts center’s announcement in May 2016 that the Broadway hit would play in Washington this summer. The women and four others bonded during their wait.

“I said afterward it was the most enjoyable waste of nine hours I’ve ever spent,” said Campbell, an Arlington resident. The Kennedy Center subscriber had already purchased a pair of tickets, but she wanted one more.

Sunday “wasn’t bad, the sun was shining. Then it started to get cold,” Dickson said. They watched the audiences and artists come and go, and many people stopped to chat. “We’d say, ‘We’re crazy, right?’ and they said, ‘No, it’s worth it,’ ” the Fairfax resident said.

Visitors to the Kennedy Center website were diverted to the “Hamilton” waiting room, as they were last month during the member sale. But this time, patrons looking for other shows could find information about them, and a phone number for non-“Hamilton” tickets was provided. “We appreciate your interest and suggest that you may have a more efficient experience tomorrow,” the website stated.

The online waiting room opened at 8 a.m., and almost immediately more than 70,000 users were queued in random order. The website seemed to be processing between 4,000 and 5,000 users an hour.

Some lucky patrons — including Michael Williams of Arlington — completed their purchases within minutes. Williams signed on to his computer at 7:58 a.m., and when sales began he was immediately in the online box office. “It was total luck,” the 24-year-old said about his purchase of four $99 tickets. He is going with two friends, so he has one unclaimed seat. “I’ll be the most popular person with my friends for the next few weeks,” he said.

Many patrons were trying for tickets in multiple ways. Katie LaWall posted on social media that she was standing in line outside the arts center when she purchased four tickets using her phone. Steve Kullen of Port Republic, Md., wasn’t as fortunate. Shut out of the member sale, Kullen tried again, but his random spot was in the upper 70,000s and he called it quits. “I think I can find better things to do than wait all day,” he wrote in an email.

The Kennedy Center’s handling of “Hamilton” has been controversial since the Tony-winning show was announced as part of the 2017-2018 theater season. Initially, officials suggested patrons needed to buy two subscriptions — to both the 2016-2017 and 2017-2018 seasons — to guarantee access to seats. The arts center also used early access to sell memberships for two seasons. That enraged some longtime and higher-level members who felt they were shut out by newcomers who paid $60 once and got in ahead of them.

The controversy continued Monday, when some fans questioned how the arts center allowed people to wait for 24 hours when their rules said “patrons may not park or sleep overnight.” A Kennedy Center spokesman said that the parking garage opened at 5 a.m. and that patrons were allowed to keep their place in line but were not permitted to sleep.

Taisje Claiborne of Upper Marlboro scored four tickets, including a pair to the closing-night performance in September. But she spent most of her 27th birthday outside the building to get them.

“I’d been doing drive-bys since Friday, looking to see if there was a line,” Claiborne said. At 11 Sunday morning, she spotted a few people in chairs, so she got in line. Her mother, Kim, joined her at 2 p.m.

“I’m super-excited, but I’m exhausted,” said Claiborne, who had taken the day off to celebrate her birthday at a spa. Instead, she pulled an all-nighter with her mom.