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BY-MO 2004 Problem 7

    A cube ABCDA1B1C1D1ABCDA_1B_1C_1D_1 is given. Find the locus of points EE on the face A1B1C1D1A_1B_1C_1D_1 for which there exists a line intersecting the lines ABAB , A1D1A_1D_1 , B1DB_1D , and ECEC .

    Dataset text AI-MO AoPS. Quoted with source.

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