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Brown v. Board of Education stands for the proposition that the equal protection clause prohibits the operation of a "dual school system" and requires the conversion of that system into a "unitary nonracial school system." Under a dual system, students are assigned to schools on the basis of their race in order to segregate them. That is clearly impermissible. But what is a permissible basis for assigning students to schools under a "unitary nonracial school system"? This seems to be the central riddle of the law of school desegregation.

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