The Washington Post's America's Most Challenging High Schools list is designed to recognize schools that challenge average students. These top-performing schools, listed in alphabetical order, were excluded from the list because, despite their exceptional quality, their admission rules and standardized test scores indicate they have few or no average students. Non-neighborhood schools with SAT or ACT averages above the highest averages for neighborhood schools nationally are placed on this list. Our sampling of private schools is exempt from this rule so that readers can see how they compare with schools on the main list.

Arkansas School for Mathematics, Sciences and the Arts (Hot Springs, Arkansas)

This two-year public boarding school was created by the state legislature in 1991. Sophomores from all over the state compete for admissions.

BASIS Chandler (Chandler, Arizona), BASIS Peoria (Peoria, Arizona) and BASIS Scottsdale (Scottsdale, Arizona)

These charter schools are among several founded by college professors Michael and Olga Block because of their dissatisfaction as parents with regular public schools. Three other BASIS schools are in the top 10 of our main list. As has happened with a few other charters, BASIS had become so popular with the parents of high-achieving students that its SAT and ACT scores put these three schools over our limit and moved them to this list. BASIS sets very high standards and has spread to other parts of the country, including the District.

Bergen County Academies (Hackensack, New Jersey)

The seven, career-focused academies have an extended school day.

Biotechnology High School (Freehold, New Jersey)

The demanding program started in 2005, with two large research rooms and four state-of-the-art science labs; most of the senior class earns International Baccalaureate diplomas.

Bronx High School of Science (New York)

One of the most famous schools in America, it has a richly talented and ethnically diverse student body.

Davidson Academy of Nevada (Reno, Nevada)

The tiny school opened in 2006 on the campus of the University of Nevada at Reno as a "university school for profoundly gifted students" under a state law.

Early College at Guilford (Greensboro, North Carolina)

At the state's first early college high school, 11th- and 12th-graders take courses at Guilford College and graduate with a high school diploma and up to two years of college credit.

Gatton Academy of Mathematics and Science (Bowling Green, Kentucky)

Juniors and seniors from around the state are selected by scores, grades and essays to live in a residence hall at Western Kentucky University, earning college credit as well as completing high school.

High Technology High School (Lincroft, New Jersey)

The school, which opened in 1991, uses the increasingly popular High Tech High name for magnets emphasizing hands-on learning. It is run by Monmouth County and Brookdale Community College.

Hunter College High School (New York)

One of the city's legendary public high schools, it has a program for seventh- through 12th-graders administered by Hunter College. It was an all-girls school until 1972.

Illinois Mathematics and Science Academy (Aurora, Illinois)

"Wayne's World," the Mike Myers "Saturday Night Live" sketch and film, is not Aurora's only claim to fame. IMSA is a state-funded boarding school. It takes 10th- through 12th-graders and has a strong mentoring program.

International Academy (Bloomfield Hills, Michigan)

The magnet school for 20 Oakland County school districts has three campuses. All students take the International Baccalaureate diploma program.

International Community School (Kirkland, Washington)

Students are selected through a lottery to attend this school focusing on international awareness. It is one of the few elite public schools without a selective admissions system. Instead, as happens sometimes, the lottery participants self-select into an academic powerhouse.

Liberal Arts and Science Academy (Austin)

Derived from two separate programs born in the 1980s, the magnet called LASA became a separate school in 2007. It draws students from all over Austin based on an application process similar to that used by very selective colleges.

Louisiana School for Math, Science and the Arts (Natchitoches, Louisiana)

Sophomores, juniors and seniors who survive the tough admissions process live at the boarding school, which was established by the state legislature in 1982.

Maggie L. Walker Governor's School for Government and International Studies (Richmond)

Unlike the math-science orientation of most of the public elites, the focus of this school is on world cultures and building students' leadership skills.

North Carolina School of Science and Mathematics (Durham, North Carolina)

This school, established in 1980 in an abandoned hospital, started the small but interesting trend of state-created boarding schools drawing bright and ambitious high-schoolers from around the state.

Northside College Prep (Chicago)

Opened in 1999, the selective magnet school was the first new high school in Chicago in 20 years. It has 1,100 students whose academic classes are at the honors and AP levels only.

Oklahoma School of Science and Mathematics (Oklahoma City)

The state-funded boarding school teaches all courses at the university level.

South Carolina Governor's School for Science and Mathematics (Hartsville, South Carolina)

Another state boarding school, this one is for 11th- and 12th-graders from around the state.

Stuyvesant High School (New York)

It has been teaching the city's most academically ambitious students for several generations. It offers about 55 AP courses every semester and has many courses above that level.

Thomas Jefferson High School for Science and Technology (Fairfax County, Virginia)

It is the second-most selective public high school in the United States (after High Technology in Lincroft, New Jersey) and draws mostly from the affluent households of Northern Virginia.

Union County Magnet High School (Scotch Plains, New Jersey)

This selective-admission school focuses on science, math and technology.

University of Illinois Laboratory High School (Urbana, Illinois)

Admission to this day school on the University of Illinois campus is competitive. The school makes good use of its higher-education environment.

Walter Payton College Prep (Chicago)

Founded in 2000 shortly after the death of Chicago Bears football legend Payton, the magnet's admission system is very competitive. The near north side school has unusually close ties with education officials in China.

Whitney High School (Cerritos, California)

Like Jefferson, this suburban version of the New York City super-schools has a highly competitive admissions system. Unlike students at the state boarding schools, those at Whitney go home at night.

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