Getting lost, in a group of lighthouses…

Let’s say you played with your friends on a flat beach with 6 lighthouses. After moving around for some time, you and your friends are too far away, so you ask them to tell you what they see in order to confirm their location. Unfortunately, based on the information they tell you, all of you can only see four of the lighthouses, and the lighthouses seen by everyone are the same ones!

After looking at the map in your hands, you realize that the positions of the lighthouses are quite random, and no three of the lighthouses are positioned in a line. In addition, you discover that these massive structures have blocked off the two other lighthouses.

Now, you’re planning on calling rescue. However, do you still remember how many friends came with you? You need to tell the rescuer the maximum number of people they need to find. What is this number?

(Problem based on the 2024 Alibaba Mathematics Competition)