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Question:

Suppose that 20 pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total number beams is:

210

190

170

180

Solution:

Total cases = number of diagonals = 20C2 - 20 = 190 - 20 = 170