The eighth-graders were razor sharp, slicing through logic problems with astonishing ease.

Problem 26: Five students are seated at a round table, facing the table. Howard is next to Tina and on her right. Jeff is next to Beth and on her right. Melinda is not sitting next to Beth. What is the seating arrangement, starting with Melinda and going to her left?

Many of the 20 or so students sitting in a classroom at Thomas Jefferson High School for Science and Technology chose the right answer in a matter of seconds: Melinda, Jeff, Beth, Howard, Tina.

"Have you been studying logic problems?" a 13-year-old girl in a pink corduroy jacket was asked after instantly choosing the correct sequence for a similar problem.

"No, I just like doing them," she said. "They just come easily."

Her mostly Hispanic and African American classmates appeared equally relaxed and confident on this sunny Saturday afternoon in October, despite the daunting goal they'd set for themselves. They were among the nearly 3,000 students from all over Northern Virginia trying to gain admission to Thomas Jefferson, a mecca for smart kids that many argue is the best public high school in the country.

The admissions process at TJ, as everyone calls the regional magnet school, has always been extremely competitive -- and controversial. White and Asian students dominated TJ's hallways for two decades. Few black and Hispanic students made the cut, and their numbers dropped precipitously in recent years. Now an effort is underway to reverse that trend and make TJ's student body more diverse. Race and ethnicity, the Fairfax County School Board declared last fall, would be among the factors weighed in selecting the fall 2005 freshman class.

The new policy was designed to boost the prospects of students such as Miguel Bustamante, a soft-spoken 13-year-old from Springfield with gelled hair and a waning Bolivian accent. Miguel was dead set on getting into TJ, which is why he'd given up a chunk of his Saturday afternoons last fall to take this 10-week test-prep course sponsored by the Parent, Teacher and Student Association's Diversity Committee. The course was aimed at preparing promising African American and Hispanic students for TJ's difficult entrance exam.

Miguel and the others plowed through an hour's worth of logic and math problems before they got restless.

"Is it time for a break yet?" someone asked.

Yeah, chirped a chorus of voices.

"This is not a democracy," replied Haywood Torrence, who teaches social studies at TJ and is the school's only black teacher. "This is a dictatorship, and I dictate when we take a break."

The words sounded tough, but the delivery was comedic, and the students giggled. There was an air of camaraderie as they worked. When one Hispanic kid correctly answered one of Torrence's questions, another belted out "Spanish power!" and pumped his fist in the air.

"People power," Torrence corrected. He directed the students to another logical-reasoning problem:

The Bump Building is taller than the Tork Building. The Tork Building and the Stump Building are the same height. All buildings in Urbanville are taller than the Stump Building. Based only on the information above, which of the following must be true? A. The Bump Building is in Urbanville. B. The Tork Building is not in Urbanville. C. At least one building in Urbanville is shorter than the Tork Building. D. The Stump Building is in Urbanville. E. All buildings in Urbanville are taller than the Bump Building.

It's simple, a boy answered: The Tork Building is not in Urbanville. Torrence wanted to know how he got the answer so quickly. "Because the contrapositive of a true statement is always true," the boy explained.

Torrence paused and asked the other eighth-graders if they understood that explanation. Nods swept the room. A few minutes later, Torrence decided it was finally time to give his students a break.

Miguel Bustamante sat at a desk in his mother's living room. Nearby was his study guide for the TJ entrance exam. He had some work to do before next Saturday's session, but right now he was thinking about robots. "A robot as smart as a human will be created by the year 2050," he'd just written in a book report for tomorrow's science class at Francis Scott Key Middle School in Springfield.

This idea pleased him for a couple of reasons. He said that maybe one day robots would be able to clean up his room. But he also liked the idea of being the engineer who could invent such wonders. Which didn't mean that he'd abandoned other career ambitions, such as astronomy and veterinary medicine. "So many things to do," he said. "I don't know yet what to choose."

Miguel longed to attend TJ. "I hear they have a robotics lab," he said.

But he had another motivation: gangs. He'd heard rumors of trouble at his home high school, Robert E. Lee. "Kids tell me it has a lot of gangs," Miguel said. Asked if that is true, Paul Regnier, a school system spokesman, wouldn't talk about Lee specifically: "Unfortunately, there is gang activity in all parts of Fairfax County . . . Students, staff members and parents in all our schools are vigilant, and largely successful, in keeping [gangs] out of our schools." Last year, Lee reported 41 fights and four weapons violations, about par for a Fairfax high school -- unless, of course, TJ is the standard: zero fights, zero weapons violations.

Miguel worried a little about TJ's lack of diversity. "It makes me unsure," he said. "Am I going to be the only [Hispanic student] there?"

In fact, he would not be. But with only a few dozen Hispanics among nearly 1,700 students, the complexion of TJ's halls would look a lot different from what Miguel was used to at his middle school, which was 25 percent Asian, 17 percent black, 22 percent Hispanic, 31 percent white and 4 percent multiracial. TJ would be different in another way. At Miguel's middle school, hundreds of kids qualified for free or reduced-price lunches, a common indicator of poverty. At TJ, just 19 students qualified.

Nora Bustamante, Miguel's mother, reached under the coffee table and pulled out an issue of Washingtonian magazine. "Top High Schools," the cover said. She leafed through the pages, halting at the one describing the demographic mix at TJ.

"There are almost no Latinos," she said in Spanish, adding wryly: "Maybe that means Miguel isn't supposed to apply?"

In her native Bolivia, Nora Bustamante studied finance at the university level. But in the United States, largely because of her limited English, she works as a nanny, a housekeeper and a caregiver for an Alzheimer's patient.

She knows she's not going to be able to afford tuition to a top college. If Miguel attended TJ, she explained, he might have a better chance at winning a scholarship: "There aren't that many opportunities for Latinos."

A team of business leaders and educators founded TJ in 1985 to train high-achieving students in science, math and technology. By almost any measure, the school has been a wild success. Last year, the average SAT score at TJ was a staggering 1482 out of 1600. According to a spokeswoman for the College Board, which administers the test, that is probably the highest average of any public or private school in the country, although such a statistic is not officially tracked. For 14 of the past 15 years, TJ has boasted more National Merit Scholarship semifinalists than any other high school in the nation. In May, the school won its fourth consecutive National Science Bowl, a competition put on by the Department of Energy involving 1,800 schools.

Set back from Braddock Road, the school building is so uninspiring that it is best evoked with two words: cement blocks. TJ outgrew its space a while ago, which explains the 13 portable classrooms in the parking lot. "We euphemistically call them 'learning cottages,' " says TJ's principal, Elizabeth Lodal.

Yet the vibrancy of this place seems irrepressible. At TJ, even the mischief and misbehavior of teenagers seems elevated. A flier advertising a student production of Shakespeare's "King Lear" last year depicted a man holding a skull. "That's Hamlet! Not Lear!" a student scrawled in black ink on the flier, which hung outside a classroom. "Corrections courtesy of Eugene." Several years ago, when graphing calculators were being stolen, Lodal discovered them being fenced on eBay.

But serious disciplinary problems are rare. Students at TJ leave their book bags on the floor all over the school. Their lockers, seldom used, seem like relics from an unenlightened era. "We have a code here that says we all trust each other," Lodal says. Which also explains why no bells herd students from class to class and why hall passes don't exist.

Still, here and there, phrases like "TJ sucks" are carved into classroom furniture. The school is a stress factory, with many students spending four to five hours a night on homework. A hand-drawn poster outside the gymnasium read: "Fatigue: How Much Sleep Do You Average Per Night?" Every year a few students quit.

But those who stick around generally do well when it's time to apply to colleges. Among the 408 members of the Class of 2004, 11 went to MIT, 10 to Princeton, 10 to Yale, nine to Stanford, nine to Duke, six to Harvard and 146 to the University of Virginia.

Asked whether TJ deserves its reputation as the nation's premier high school, Harvard's director of admissions, Marlyn McGrath Lewis, says, "Let me put it this way: A lot of the people on my staff, if they lived in Northern Virginia, would want to send their kids to TJ."

For a long time, the admissions process at TJ varied little. In the fall, hundreds of eighth-grade applicants took a multiple-choice test. The results were combined with grade-point averages to form scores. Students with the 800 highest scores passed to the next round. Then a series of committees would evaluate the applicants using additional information, including essays and teacher recommendations, finally selecting more than 400 students for admission.

For many years, TJ accepted black and Hispanic students who didn't quite make the top 800 but came close and had good grades. Then the federal courts struck down several affirmative action programs at schools around the country, and attorneys advised TJ's administrators to end any racial or ethnic preferences. The result: From 1997 to 2001, the number of Hispanic students in TJ's freshman class fell from 24 to seven. During the same period, the number of African American freshmen plummeted from 25 to two.

At that point, Lodal described the number of blacks and Hispanics being admitted to TJ as "indefensible on every level." Now heading into her sixth year running TJ, the ebullient Texas native, who studied math and physics at Rice University, has been an outspoken advocate for increasing the presence of those minorities.

Daniel Domenech, then Fairfax County's schools superintendent, also expressed alarm about the decrease in diversity and suggested several ways to boost Hispanic and African American enrollment. One proposal would have allotted each county middle school a prorated share of freshman slots; traditionally, middle schools in largely white and affluent parts of the county have sent students to TJ in far higher numbers than middle schools in poorer areas with higher concentrations of minorities. Ultimately, the school board set aside up to 30 spaces for students from underrepresented middle schools -- a strategy that didn't accomplish much. In 2002, only one of the spaces ended up going to an African American.

Yet it was a white parent who raised the loudest ruckus over TJ's admissions practices. Two years ago Lloyd Cohen, a law professor at George Mason University and a parent of two TJ students plus another who'd been rejected, wrote an analysis of the school's admissions policy in the Albany Law Review. Using data amassed through the Freedom of Information Act, he found that 91 percent of African Americans who passed to the second round were admitted to the Class of 2006, or 10 of 11 students. Meanwhile, 49 percent of white students in the second round were admitted, or 249 of 507 students. Cohen accused the school of having a policy of surreptitious racial preferences. He called it "invidious racial discrimination."

Superintendent Domenech fired back with his own article in the Albany Law Review: "I must respond to the offensive and untrue implication that the African American students at TJ are less qualified than their white counterparts . . . Careful analysis of the data demonstrates clearly that there is no meaningful difference between the test scores and qualifications of the African American students and those of most of the white students admitted to TJ."

The animosity deepened when TJ's student government president invited Cohen to the school to present his findings, and Lodal promptly canceled the event. At the time, she asked, "How could any educator approve of allowing a situation where a group of their students would be publicly demeaned?"

Later Lodal assembled a panel of outside experts to discuss, during the school day, the pros and cons of affirmative action. Cohen was not invited. He did, however, file a complaint against the school with the office for civil rights at the federal Department of Education. The complaint, according to an Education Department spokesman, is still being considered.

Meanwhile, black and Hispanic students continued to make up a tiny fraction of TJ's student body. Determined to change that, the Fairfax County School Board voted last September to overhaul TJ's admissions policy. Gone was the old formula for passing 800 students to the second round. Under the new formula, an undetermined number of students could advance, based on a sliding scale of GPA and test score. For example, a student with a GPA of 2.67 would need a test score of 90 percent, while a student with a GPA of 3.67 would need a test score of only 60 percent. It was estimated that 1,500 students might now make the second round. The idea was to pass as many applicants as seemed reasonably qualified to the second round, where they could be judged on more subjective criteria, particularly essays and teacher recommendations.

The school board made one other big change: The selection committees could consider applicants' race and ethnicity when deciding whether to offer admission. It also should look for diversity in the areas of "gender, English for speakers of other languages, geography, poverty, prior school and cultural experiences, and other unique skills and experiences." School system officials said this would be done without any illegal quotas, point systems or predetermined weights for any one group.

The timing of the new admissions policy was key. In June 2003, the Supreme Court had upheld the race-conscious admissions policy of the University of Michigan Law School, citing "the educational benefits that flow from a diverse student body." The Fairfax school board seized on the language used in that decision. TJ needed diversity, the board said, not in the name of social justice, but in the service of forging a richer learning climate.

Not everyone agreed with this reasoning. "If TJ was a magnet school for public policy and international relations, I could see why more racial diversity would make sense," says Louise Epstein, whose daughter will be an 11th-grader there this year. "But TJ is supposed to be a math, science and technology school. Race is irrelevant when you're trying to solve a math or physics problem or figure out an efficient computer program."

School officials insisted that the push for diversity was not just code for changing the racial and ethnic mix at the school. Rather, TJ was trying to open its doors to a whole slew of kids who, while perhaps not the greatest on standardized tests, are risk takers, curious and resilient. In other words, kids who have the potential to form a new generation of scientific leadership.

But Cohen's appraisal of the new policy was unsparing. "It embodies all the evils and idiocies I expected," he wrote in a recent e-mail. "It is much worse than what I railed against."

Kiara Savage had given up countless Saturdays getting ready for the TJ entrance test. Her prep course -- separate from the one Miguel Bustamante was taking -- was the culmination of a two-year science and math enrichment program called Quest, which was launched by the Fairfax school system in 1998, partly to boost the enrollment of high-achieving, underrepresented minorities at TJ.

Kiara was an eighth-grader at Rachel Carson Middle School in Herndon, and one of the few African American students in its gifted and talented program. Her mother, Pat Savage, loved to boast about Kiara's accomplishments.

"Kiara is very time-disciplined," Savage said. "It's amazing for her to be playing two high-level sports" -- basketball and soccer -- "and still be able to get a 4.0 in gifted and talented classes."

Kiara, 13, looked back happily on her two years in Quest. "I go to a school where there aren't a lot of other African American students," she explained. "So going to Quest every other Saturday helped me get to know some other African American students in the area. Also, there were a lot of nice teachers there -- they really cared about getting us into TJ."

But along the way, she figured out that maybe science, math and technology, weren't her real loves. "Actually, I'm not big into science," she said. "I can cope with it. I can do science, but I actually like English better." Recently she'd trailed around with a reporter from ABC News, and she'd decided that journalism was her calling.

She also felt some ambivalence toward TJ. "I know I'm a pretty good student," she said. "But when I think of students at TJ, I think of students who are constantly in the books, constantly studying." Was that the kind of high school experience she was looking for? She wasn't sure. Perhaps she wouldn't go to TJ, even if she got in.

The lack of diversity at TJ didn't really disturb her. "I'm used to that, not having a lot of African Americans in my classes," Kiara said, though she'd experienced the indignities that sometimes accompanied being different. "A lot of my friends will say things like, 'Kiara you're the smartest black person I know.' " These friends weren't trying to be racist, she said, even if it came off that way.

Kiara's mother, an acquisitions analyst for a defense contractor, and her father, Keith, a funeral director, also felt uncertain about their daughter going to TJ. Kiara's home school, Chantilly High, offered an excellent education and was less than a mile from the Savage home. TJ, on the other hand, was a cross-county haul. With traffic, the drive could take close to an hour each way. TJ employs a network of buses that shuttle kids from across Northern Virginia; two-hour commutes are common. Kiara's parents weren't thrilled with the thought of their daughter spending so much time on the school bus. They would probably end up shuttling her themselves. Was it worth it? The Savages really weren't sure.

On test day last December, Miguel Bustamante woke up before his mother and cooked himself some eggs. He mainly wanted to be a scientist, yes, but he also liked the idea of being a chef. Two years ago, he'd surprised his mother on her birthday by making cinnamon knots and serving them to her in bed. "I was sleeping, and I didn't suspect a thing," Nora Bustamante recalled. "How delicious."

The delight of being served breakfast in bed was heightened by the long years she'd spent apart from Miguel and his older brother, Jose. Bustamante and her husband left Bolivia in 1991 for a better life in the United States. Miguel and Jose stayed behind with their grandparents. For the next decade, Bustamante knew her sons only by mail, phone calls and, later, Internet video conferences. The separation tormented her, she said, though the money she was earning paid for Miguel's tuition at a private school, where he learned rudimentary English. Then, in 2001, the Bustamantes were finally able to bring Miguel and Jose to the United States.

The Bustamantes live in a townhouse in Springfield, within earshot of Interstate 95, on a street lined with mature oaks. Miguel's parents jointly own the home, although they have been separated for three years. Miguel's father lives in the basement, waiting for the divorce to be finalized.

Miguel and his dad were not close, the eighth-grader said. It was his mother and 21-year-old brother, Jose -- a student at Northern Virginia Community College who worked as a Domino's Pizza driver -- who prodded him about schoolwork. Often he needed it. Miguel tended to watch TV while doing homework or intersperse studying with video-game sessions. While he was preparing for the TJ test, Jose hid the games for his little brother's PlayStation 2, and told Miguel he was only allowed to play on weekends.

"He was starting to play it all the time, and I didn't like that," said Jose, who hopes to finish his bachelor's degree at George Mason University. "If he wants to be in a comfortable situation in the future, I think he needs to study now."

After months of buckling down, Miguel said he felt ready for the TJ test. At least the math section. "But I'm afraid the verbal is going to be too hard."

When he arrived in the United States, he hardly spoke any English. On the first day at his Fairfax elementary school, "I knew how to say 'blouse,' 'pants' and 'Hello, how are you,' " Miguel recalled. He remembered wondering, How am I going to understand the teacher? "What am I going to do? What am I going to write? But the teachers helped me a lot." Still, until his English improved, it was tough making friends.

Now Miguel speaks English at a clip, with a faint accent. Last year, he stopped taking ESL classes. And this year, given his A's in most classes, one of his teachers had recommended him for the gifted and talented program at Key Middle School. Still, he worried that his vocabulary wouldn't measure up.

On test day, Miguel's mother drove him to one of the TJ testing sites. Miguel breezed through the math section, he later said, though when he compared notes afterward with a middle school friend, he realized that he'd messed up one problem dealing with triangles. He didn't worry too much because it seemed like he'd understood most of the problems.

Miguel said the essays went okay, too. But the vocabulary, as predicted, proved to be a challenge. Some words he simply didn't know. Later he tried to recall some of the words that had stumped him. He thought about it and shook his head. No luck; the words had vanished like smoke.

By early winter, Miguel was growing anxious to hear a response from TJ. Every day he watched his mother sort through the mail. "Mami, hay algo para mi?" Nora Bustamante remembers him asking. Mom, anything for me?

Miguel knew that some kids at Key had already gotten their letters. Most hadn't made it to the second round. Miguel was starting to doubt whether he would, either.

Then one day, when Miguel was doing his homework and watching TV, his mother came into the living room. "There's a letter from Thomas Jefferson," she said. Miguel tore it open. It was the same letter that 1,600 other students across Northern Virginia were receiving. It was the same letter that Kiara Savage was receiving. The letter said that he had passed the TJ test; he was going to the second round. Miguel and his mother threw their arms around each other.

Kiara Savage was riding home on the school bus one day, not long after receiving her letter from TJ, when she overheard another student talking about the school. "They made the admissions process easier so black people and Hispanic people can get into the school," she recalled hearing the boy say.

She tapped him on the shoulder. Excuse me, she said. TJ is a very prestigious school. The people who run it would not lower the standards just so they could add 50 more African Americans to their school.

Trying not to lose her cool, she reminded herself of her 4.0 GPA, the countless hours she'd spent on the basketball court and soccer field, her two years of extracurricular math and science courses. She'd thrived on hard work -- and for all those reasons, she explained to the boy, she deserved every nod that came her way.

"Are you calling me a racist?" the boy demanded.

"No, I'm just trying say that some of the things you're saying may be interpreted by some people as racist."

That evening Kiara told her mother about the incident, which prompted Pat Savage to share her own experiences as a political science major at Virginia Tech in the early 1980s. "People made snide remarks, saying I got in because I was black," she said. She told Kiara that if she went to TJ, "there's going to be people who think you're there just because of your race . . . They're going to make that assumption, so you've got to be prepared to stand up for yourself and say, 'You know what, I bet my credentials match up very nicely with yours.' "

Jose Chaparo, a 17-year-old junior at TJ, walked into his second class of the day, "chemical analysis research laboratory." A classmate, slumped at his desk, looked up and said that he liked Jose's shirt. Thanks, Jose said. He'd brought it back recently from Bogota, where he'd lived until five years ago. Along with his parents, both engineers who'd worked for American companies, he emigrated to Northern Virginia to escape the violence seizing Colombia. He'd gone to a bilingual school in Bogota, but "I was by no means fluent in English . . . You don't know a language until you really have to use it."

Jose slipped to the back of the room, putting on a lab coat. Most of his courses, he said, were a lecture format, and he'd just sat through a 90-minute physics class that had put one student to sleep. Jose considered himself more of a chemistry guy anyway, making this class one of his favorites. "You get to work with your hands," he said, strapping on protective goggles and flipping the power switch on a spectrometer.

TJ has 12 specialized laboratories where upperclassmen can conduct independent research projects. In the automation and robotics laboratory, for example, one recent student project involved building an all-terrain walking robot. Jose's project, which he'd been plugging away at for months, involved measuring fructose levels in sports drinks. Today his research was bumping into a rough patch; certain measurements he'd taken were not jibing with published data, and he forced himself to scrap several days of work for a fresh start. "It's definitely student-driven," Jose said. "You're free to do as you like." As he spoke, the instructor was nowhere in sight.

Jose said that he didn't pay much attention to the diversity debate at TJ. But he worried that efforts to diversify the school might undermine the quality of students. He and his family had chosen this school, he said, because it was the most academically challenging in the area. "If you lower the standard, it all goes down," he said. "We had to put up with a hard standard. Why shouldn't they?"

Jose dropped a glass tube into the spectrometer and said that he didn't mind having few fellow Latino students around. "There's one other kid from Colombia," he said. "Natalia something. I met her freshman year. She probably still goes here, but I don't know . . . I don't yearn for any kind of Latino-ness."

The Robot Club, the Gay and Straight Alliance, and the Fellowship of Christian Athletes convene during eighth period at TJ. In the hallway, a poster for one club invites students to discuss the struggle for Tibetan independence, while another club simply shows reruns of "The Simpsons." There's also the Asian Awareness Club, the Scottish-Irish Culture Club and the Black Student Union, whose members gathered one spring afternoon in the classroom of one of their faculty sponsors, Melissa Schoeplein.

"It's very embarrassing to be 10 miles from the Lincoln Memorial, where Martin Luther King gave his speech, and to have a school with so few black students," said Schoeplein, who is white and teaches government.

The meeting attracted 11 students, including a sandy-haired, blue-eyed sophomore who had tagged along with a friend. The rest were African American and represented about half of the school's black population.

Senior David Sneed, one of only three black members of the Class of 2005, sauntered up to the front of the room to talk about his college-application experience. He clutched a Tar Heels jersey and said that attending the University of North Carolina had been a lifelong dream. Now he'd been accepted and was a finalist for a Robertson Scholarship, an honor that he would end up winning a few days later, meaning a full ride plus a four-year stipend.

"Can you tell us about your college essay?" called out Schoeplein.

Sneed smiled and told the underclassmen that his essay had been about his first day at TJ. It was the fall of 2001, when the number of black students in the freshman class hit an all time low. He'd come from Lake Braddock Secondary School, where there were more than 200 African American middle and high school students.

"It took me until the last period of the day, seventh period, before I saw another African American face in my class," he wrote in his essay. "While the environment was in no way hostile or unfriendly, I realized in my freshman year that I had entered into a community unlike any other I had ever encountered. Walking through the halls each African American would not hesitate to greet one another, faculty and student, understanding the feelings of singularity in classes, activities and offices around the school."

He often found himself mistaken for a different black guy. "That happens all the time," he said in an interview. "People confuse us; they think we're the same person." But he added that he has in no way felt marginalized over the past four years. "I truly love this school," he said. "It is an amazing place."

He loved it so much that he spent countless hours on Saturday working with kids in Quest, the enrichment program that Kiara Savage participated in.

"What we're trying to do is not make it so less-educated or less-qualified students get into this school, just because they're African American or Latino," said Sneed, a Quest graduate himself. "The point is to help this school become a better place and better environment. Eventually, students are going to have to deal with people of different races, not only different races but different perspectives. So being able to deal with a wide variety of people is a valuable skill that you'll be able to use throughout your life."

Once he'd made it to the second round, Miguel handed three of his teachers recommendation requests, and filled out a form describing his interest in math and science. Then he waited.

One afternoon in early April, he was digging through the pile of mail that his mother had left on the table and found a letter from TJ. He called out to his mother, who hurried into the room. Together, they opened the letter. First, his mom read it. Then she handed it to Miguel:

"The selection committees have completed their review of the applications for admission to the 2005-2006 freshman class . . . " A prosaic opening, never a good sign. ". . . I am sorry to report that you have not been selected for admission . . . I wish you continued academic success . . . Thank you for considering TJHSST as a high school option." The results from his test in December were enclosed. On the math portion he had scored in the 74th percentile. And on the verbal he'd scored in the 38th percentile.

His mom hugged him and said that he should be proud of even making the second round. Miguel felt a little shellshocked. "I thought I was going to get in," he said. "I thought that they would need some Spanish" students.

But Miguel's disappointment didn't last long. He signed up for classes at Lee High School and said he's no longer worried about going there. Some of his middle school teachers, he said, have assured him that gangs are not a serious problem. Nora Bustamante wasn't exactly giving Lee rave reviews. Last year its students scored an average of 1025 on the SAT -- more than 450 points lower than TJ's average. "I was reading the Washingtonian -- the best high schools -- and it's toward the bottom of the rankings," she said. But Miguel has signed up for the International Baccalaureate program, which will put him in classes with Lee's smartest and most ambitious students.

In the meantime, summer was approaching, and Miguel was hunting for camps that might capture his imagination. Then he found the ideal camp. A summer camp at Edison High School. One of its main activities: building robots.

Kiara knew the final letter from TJ was due at any time. But she couldn't check the mailbox each day because her mother had the key to it. Besides, she wasn't really worried about getting in. All her friends were chattering about Chantilly High. More than ever, Kiara wanted to go there with them.

She was doing her homework one night in early April when her mother came home from work, holding an open envelope. "I'm sorry, Kiara, you didn't make it in," Savage told her. Kiara remembered feeling disappointed but not shattered. Now she wouldn't have to choose between TJ and Chantilly.

Then Savage handed the letter to Kiara, so that she could read the bad news for herself. That's when Kiara started laughing. One would think she could detect her mom's practical jokes by now. Obviously not. It wasn't a rejection letter -- TJ had accepted her.

"It was almost bittersweet," Kiara said. "I was excited that I got in -- I was excited that as an African American student I got in -- but also I knew that I needed to make a decision between the local high school that I'd started to fall in love with and TJ."

A few weeks later, Kiara and her mother drove to TJ for a welcome night for incoming freshman. A quartet of students was playing Mozart in the lobby. Others, representing various student organizations, were trying to lure the newbies. "Welcome to TJ," said one student. "Have you ever heard of the Color Guard?"

Kiara and Pat Savage stopped by the cafeteria, where there were even more organizations seeking fresh members. They picked up a registration packet and then stopped by the Black Student Union table, which was next to the football team's. Kiara listened to a pitch for joining the club. Joining the club? Kiara wasn't sure she wanted to join the school.

Down the hall from the cafeteria, Elizabeth Lodal was in the office saying hello to a few new parents and students, including the boy who'd known that "the contrapositive of a true statement is always true."

It had been a record year for applications: 2,902, including 227 Hispanics and African Americans. A total of 1,601 kids had made it to the second round of the selection process, among them 82 Hispanics and 37 African Americans. Now the school had offered admission to 495 teenagers: 262 whites, 160 Asians, 19 Hispanics, 12 African Americans, three Native Americans, 31 multiracial students and eight marked "other."

As it turned out, the new admissions policy hadn't made a dramatic impact on the racial and ethnic mix at TJ. "I was pleased to see that we had 12 [African American students] accepted," Lodal said, one more than the previous year. "I would have been happier if we'd had 20. The big leap forward were the Hispanic students," whose numbers nearly doubled. That "was a very nice thing to see, and wonderful."

But the overall imbalance at the school still seemed to worry her: "I don't think we yet have enough of the critical mass, either in the numbers applying or in the numbers accepted, to truly make a statement that's clear to the minority communities, the underrepresented minority communities, that this is a school for you and we want you here."

Not long after welcome night, Pat Savage had a talk with Kiara. "I'm gonna be real with you," she remembers telling her daughter. "Mom and Dad are not going to be able to send you to any college that you want." Lately, Kiara had been saying that she wanted to go to Duke, where tuition alone is more than $30,000 a year.

"You might get into Duke," Savage said. But paying for it would be a problem. "I need [Duke] to call you and say, 'What can we do to get you here?' " In other words, Kiara needs to rake in some big-time scholarship offers by the time she finishes high school. And TJ was a better bet for doing that than Chantilly, her mother told her.

Kiara listened and made her choice. This fall, she'll be a freshman at TJ.

Tyler Currie is a contributing writer at the Magazine. He will be fielding questions and comments about this article Monday at 1 p.m. at