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HMMT November 2020 E3

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Jody has 6 distinguishable balls and 6 distinguishable sticks, all of the same length. How many ways are there to use the sticks to connect the balls so that two disjoint non-interlocking triangles are formed? Consider rotations and reflections of the same arrangement to be indistinguishable.

Dataset text NuminaMath olympiads. Quoted with source.

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7200

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