first i think u mean where do all The Hunger Games tributes live? and they first live on a train for each district and then when the actual Hunger Games start they live in a forest.
---- Sara
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They are called Tributes
they go to the capital city, where they get groomed and trained for the upcoming hunger games. then, they are lifted into an arena, where they have to fight for survival. sources: watched the movie
Cashmere and Gloss are the brother and sister tributes from District 1 in the 75th Hunger Games.
the reaping
This is called the Reaping.