Felicity has 20 thin rods whose lengths, in centimeters are 1, 2, 3 …., 20. Any two rods can be connected at their ends. Felicity selects three rods to make a triangle, then three other rods to make a second triangle and so on. a. Only 1 of Felicity's rods cannot be the side of a triangle. Determine which one.
b. Felicity 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.