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AUSTRIAN-POLISH 1987 Problem 8

    A circle of perimeter 11 has been dissected into four equal arcs B1,B2,B3,B4B_1, B_2, B_3, B_4 . A closed smooth non-selfintersecting curve CC has been composed of translates of these arcs (each BjB_j possibly occurring several times). Prove that the length of CC is an integer.

    Dataset text AI-MO AoPS. Quoted with source.

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