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HMMT November 2018 H9

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Circle ω1\omega_{1} of radius 1 and circle ω2\omega_{2} of radius 2 are concentric. Godzilla inscribes square CASHC A S H in ω1\omega_{1} and regular pentagon MONEYM O N E Y in ω2\omega_{2}. It then writes down all 20 (not necessarily distinct) distances between a vertex of CASHC A S H and a vertex of MONEYM O N E Y and multiplies them all together. What is the maximum possible value of his result?

Dataset text NuminaMath olympiads. Quoted with source.

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2^{20}+1

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