Problem

Source:

Tags: linear algebra, matrix, function, inequalities, combinatorics



Set $T$ consists of $66$ points in plane, and $P$ consists of $16$ lines in plane. Pair $(A,l)$ is good if $A \in T$, $l \in P$ and $A \in l$. Prove that maximum number of good pairs is no greater than $159$, and prove that there exits configuration with exactly $159$ good pairs.