Gunmen in the room with wall and empty spaces

Question

There is a room with n rows and n columns, and there are gunmen in the room.
A gunman can see vertical or horizontal way, and cannot see over the wall or diagonal.
If a gunman see another gunman, they will shoot each other and only one man will survive.
We want all gunmen to be alive.
■: Wall
□: Empty space
1: Gunman

For example, there is a room with 4 rows and 4 columns,
■■■□
□□□□
□■□□
■■■□

we can place 3 gunmen like below.
■■■□
□□□1
1■1□
■■■□

However, we cannot place gunmen like below, because they are in the same line horizontally, one man will die.
■■■□
□1□1
□■□□
■■■□

We can place maximum 4 gunmen in this room, and there are 2 ways to achieve this.
■■■1
□1□□
1■1□
■■■□

■■■□
□1□□
1■1□
■■■1

Input for question 2.1 and 2.2
□■□■□■□■
□□□□□■□□
■□■□□■□■
□□□□□□□□
□□□■□□□□
□□□□□■□■
□■□□□□□□
□□□□■□■□

2.1 What is the maximum number of gunmen we can place in the room above? *

2.2 How many ways to place maximum number of gunmen? You have to calculate all possible ways. *

Don't forget to include your workings and explain how you go about solving this problem.

Bunuel · Answer

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Gunmen in the room with wall and empty spaces

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