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Omni-MATH / How many ways are there to arrange the numbers 1,2,3,4,5,6 on the vertices of a regular hexagon such that exactly 3 of the numbers are larger than both of their neighbors? Rotation…

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problem

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.
Plain-text mathematical notation (without MathML)
How many ways are there to arrange the numbers 1,2,3,4,5,6 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.
Original LaTeX notation
How many ways are there to arrange the numbers $1,2,3,4,5,6$ 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.

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