Ok so this is the easy way
Put your back to the gun #1 is the tower right in front of you #2 is the next outside tower connected to #1 - #3 is the last outside tower connected to #2
Keep in mind this is layed out like your numerical keypad on your keyboard
So that means #4 is to the left of you and the gun just north of the elite and add-on #5 and #6 to follow
#7 is ------- yes the tower between the 2 elites just left of the gun which means #8 and #9 are the two other outside towers #9 being the group of 4 npcs
go to this link - http://www.ueda.info.waseda.ac.jp/~n-kato/lightsout/index.html
Select 3x3 - select edit - Red is off and blue is On
Look at whats on and whats off - looking at the 3x3 grid
123
456
789
Once you select all of that click play then solve go and click on the towers that show 1's from the site and your done.