“It is a challenge, but it’s the kind of challenge that I think the university is glad to have,” said Mark Owczarski, a Virginia Tech spokesman. Facing under-enrollment would be a bigger problem, he said. “What it speaks to is, people really want to be at Virginia Tech,” he said.

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School officials are calling it “the Amazon effect” because of the school’s planned $1 billion graduate campus near Amazon’s planned headquarters in Northern Virginia, a prospect that university officials say is attractive to students.

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But the mayor of Blacksburg, Va. — home of Virginia Tech’s main campus — described it as an emergency for a rural town dwarfed by the state university.

“We have three months to find some place to house all these freshmen,” Mayor Leslie Hager-Smith said. “A thousand people in a very small town,” one with next to no available housing stock and very few rental vacancies. “There aren’t places for people to go. They don’t exist.”

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College freshmen represent a vulnerable population, she said, not just at Virginia Tech but nationally, with fewer life skills and, in some cases, mental health problems.

The mayor said she has weekly meetings planned with the university’s top leaders to grapple with the situation. “We are their allies; we want to see them succeed,” Hager-Smith said. “But it’s important for them to understand the limitations."

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Owczarski said Virginia Tech’s applicant pool was the second-largest ever, numbering more than 30,000. The school hoped to have an incoming class of 7,000 students, anticipating that about 400 would drift on to other plans over the summer — the typical “summer melt” — leaving 6,600 students.

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The number of students accepting admission offers was on track all spring, Owczarski said — up until April 26, when the school usually sees a decline.

This year, it didn’t: People kept saying yes. Roughly 8,000 of them.

Virginia Tech plans to build a 1-million-square-foot Innovation Campus in Alexandria to educate hundreds of graduate students in computer science and software engineering, with specializations in areas including artificial intelligence, cybersecurity and data analytics.

That prospect may have made the school more attractive, Owczarski said. “Our enrollment numbers are highest in computer science, computer engineering and related . . . fields,” he said.

Whatever the reason, the booming enrollment figures could have implications for housing, dining, hiring, academics and other areas, so university officials are working on ways to combat the potential complications.

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In recent days, officials sent emails to 1,500 incoming freshmen, offering incentives to delay enrolling. They anticipate that could cost the school more than $3 million.

Laura B. Osberger, spokeswoman for the State Council of Higher Education for Virginia, said the organization is not aware of other colleges in the state having offered financial compensation to students who defer admissions.

Mike Reilly, executive director of the American Association of Collegiate Registrars and Admissions Officers, said he wasn’t familiar with another example nationally. College officials are always trying to hit enrollment targets, he said, and there’s usually some predictability to those numbers. But sometimes when they try something new — such as adding a scholarship — they might find more students choosing to enroll and have to adjust, he said.

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Schools occasionally have to scramble to find more instructors and add sections of first-year classes, Reilly said. They might also ask students to defer enrolling until spring semester, or to temporarily take classes at a branch campus. Schools that require freshmen to live on campus sometimes add beds to double rooms, he said — hardly an ideal solution.

At Virginia Tech, officials have waived the requirement that freshmen live on campus this fall, and told other students who have signed university housing contracts they can make other plans if they would like.

Hager-Smith said Blacksburg consistently has a low rental vacancy rate, but this year is particularly challenging because some apartments are being redeveloped and aren’t available.

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“I do trust — I have faith,” she said of school officials. “I believe that they are scrambling to do every inventive thing that they can do.”

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The University of California at Irvine shocked hundreds of students in 2017 when the school rescinded admission offers two months before school began.

“That was bad form,” Reilly said. “You can’t do that.”