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The numbers 1 to 9 are placed on the sides and corners of a triangle so that every side sums to 17. How many distinct arrangements are there?

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The integers 1 to 9 are placed along the sides and vertices of an equilateral triangle, with each vertex number counting towards both adjacent sides. If every side (including its vertices) sums to 17, how many distinct arrangements are there, ignoring rotations and the order of numbers within a side?

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