Problem
COM-B1-M04-P023 Points and Lines
#23
★★★★☆ Level 4 of 5
There are \(9\) lines, each with \(5\) marked points. Each marked point lies on exactly \(3\) lines. Find the number of marked points.
Count incidences \((point,line)\).
By lines, there are \(9\cdot5=45\) incidences. If there are \(N\) points, counting by points gives \(3N\). Thus \(3N=45\), so \(N=15\).
Pure incidence-counting problem.