Problem 5
Suppose five points in a plane are situated so that no two of the straight lines joining them are parallel, perpendicular, or coincident. From each point perpendiculars are drawn to all the lines joining the other four points. Determine the maximum number of intersections that these perpendiculars can have.
Step 3 of 5: Correct the pair count
Detailed analysis
Summing the bound over all perpendiculars counts each ordinary intersection twice, once for each line. Therefore there are at most ordinary intersections.