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HMMT November 2022 E2

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How many ways are there to arrange the numbers 1,2,3,4,5,61,2,3,4,5,6 on the vertices of a regular hexagon such that exactly 3 of the numbers are larger than both of their neighbors? Rotations and reflections are considered the same.

Dataset text NuminaMath olympiads. Quoted with source.

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