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Does there exist a set M ? (IMO SL 1987-P9)

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August 19, 2010
algebrapolynomialanalytic geometryIntersection3D geometryIMO Shortlist

Problem Statement

Does there exist a set MM in usual Euclidean space such that for every plane λ\lambda the intersection M∩λM \cap \lambda is finite and nonempty ?
Proposed by Hungary.
[hide="Remark"]I'm not sure I'm posting this in a right Forum.
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