Being furloughed without pay through October and most of November was a nightmare for federal workers across the U.S. But for Emma, who lives in Chelsea with her twin eighth-graders (and asked to use a pseudonym), the break had a silver lining: It gave her the time she needed — though many parents might argue that no amount of time is truly enough — for the singularly painstaking task of applying to New York City’s public high schools.

In some American cities, teenagers seeking a specific curriculum have the option of applying to high schools in lieu of going to the one closest to their home. Only in New York is this process the standard operating procedure for every public school student. The city’s public-education system houses seven categories of admission methods with strangely opa

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