MathDB

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.

Problem Statement