DE-BUNDESWETTBEWERB 2023 Problem 6

A hilly island has $2023$ lookouts. It is known that each of them is in line of sight with at least $42$ of the other lookouts. For any two distinct lookouts $X$ and $Y$ there is a positive integer $n$ and lookouts $A_1,A_2,\dots,A_{n+1}$ such that $A_1=X$ and $A_{n+1}=Y$ and $A_1$ is in line of sight with $A_2$ , $A_2$ with $A_3$ , $\dots$ and $A_n$ with $A_{n+1}$ . The smallest such number $n$ is called the viewing distance of $X$ and $Y$ .

Determine the largest possible viewing distance that can exist between two lookouts under these conditions.