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pierce,
Perhaps, instead of killing the 200 babies, you should have a lottery to randomly select 200 people to kill; or you could institute a competitive event (such as dueling) which will serve to limit the population; or you could eliminate the least productive adults, or criminals, etc.
You also need to implement a policy to limit future population growth, such as allowing only as many births as deaths in future years. Anyone who has an illegal child gets put on a raft and floated out to sea.
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