As the possibilities multiplied, so did the sense of mystery. Maybe they were homeless people; the Census Bureau was not sure. Perhaps they were municipal workers who lived above a maintenance shed; parks officials said it was impossible. City planners were stumped, too.

Who were they, then, these two-dozen-plus urban pastoralists who had told census takers, in the count last year, that their address was none other than Central Park? Bench-dwellers? Gentry displaced from the Dakota? Schnauzer owners on an endless stroll? No one knew.

All that was certain — if, indeed, anything was — was that New York City Census Tract No. 143, better known as Central Park, was officially home to 25 residents in 2010. Not only were there enough of them to stage a football game, but their ranks had also apparently increased: a stunning 39 percent, in fact, over the previous decade, dwarfing the 2.1 percent growth in the city’s overall population. While the island of Manhattan had become ever whiter since 2000, Tract 143’s black population had doubled. The number of Hispanics, meanwhile, had ballooned by 500 percent.

With the authorities unable to provide clear answers, the only recourse seemed to be a brisk walk through the park in search of dwellers — or, at least, potential dwellings.