Answers:
Go to basically any college and take up computer science/engineering. Since you want to be a video game programmer, use your free classes trying to extend your understanding of video game design, like taking a game design class or graphic design class if the college offers it. Since the needs of video game development teams are so broad, anything you learn can be applied to making video games.
I wouldn't recommend going to specialized colleges and programs, because then you would be stuck in video games (good idea now, but later on..). Build up skills in video games and other areas just in case your plan doesn't seem so good later on
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