Paul has 20 thin rods whose lengths, in centimetres are 1, 2, 3, ..., 20. Any two rods can be connected at their ends. Paul selects three rods to make a triangle, then three other rods to make a second triangle, and so on. Question: Paul wants to use 18 rods to form a set of six triangles with equal perimeters. Either find such a set or explain why no such set exists.

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