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Question

The figure below represents a figure with a total of 120 triangles and n points labeled as vertices on the horizontal base. What is the value of n? FIGURE

Accepted Answer

Since any two points A_i,A_j define exactly one triangle, there are n2 = n(n-1)2 possible triangles. Solving n(n-1)2 = 120, we find that n = 16.