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Well it was definitely Pre-Games I'd say a good 50 to 200 years before the games would have began. The wiki said this "Panem eventually grew large enough that it was segmented into thirteen separate districts, each responsible for producing goods of a particular industry to serve the growing needs of the nation, and all operating under the auspices of Panem's oppressive Capitol. Its exact method of expansion is unknown; it is possible that some of the separate districts may have even once been smaller, separate nations that were eventually annexed by Panem." Perhaps around this time the Districts were locking into place - say we put it a good 200 years before the games, that would be about 140 years before the destruction and rebellion of District 13 - so people began to move toward what they new best because they were going to be enclosed in one district for the rest of their lives?