The buildings are not identical; they have different configurations and capacities, with apartments ranging from two bedrooms to five. Delegations might request a building close to the dining hall or the gym, only to accept a secondary choice farther away if it meant having a building all to themselves.

“Some really like to take ownership of their space,” Cilenti said.

The United States is one such country. It wanted a building that was conveniently situated but without a lot of distracting pedestrian traffic nearby.

“In this village, there were a number of places that might have been a more strategic location — closer to the transportation and the dining room — but it would have meant dividing us into two buildings,” said Leslie Gamez, the United States Olympic Committee’s managing director of international games. “In this case, they said that this building can hold about 900 people, which is what we knew our delegation would be.”

Russia and China, next-door neighbors, are among the other sole occupants of buildings, although Russia has dozens of empty rooms, a result of the doping scandal that knocked more than 100 of its athletes out of the Games.

Most delegations gleefully reveal their locations with flags and banners, giving color, and a bit of a hanging-laundry vibe, to the compound. All displays required approval to ensure that they did not hinder fire safety, obstruct vents or views, or become safety hazards of any sort.

Russia draped its building in giant flags. China pressed identical flags on the inside of each glass balcony, a more disciplined display. Australia striped its building with vertical, nine-story yellow banners that read “Australia.”