I noticed a building outside my house with randomly lit rooms and dark rooms. If I treat each one of those windows as a square, is it possible to calculate the total number of patterns that can be created by illuminated rooms. Say there are 25 windows in total. (5*5) I don't know if I'm being articulate enough with my problem.
I tried using Combinations, but I'm not sure how to approach it properly.
In a 2*2 matrix, the number of patterns that can be created is 12.(Including the pattern where none of the rooms are lit). I calculated this without using a formula, just by logic. Is there a simple method I can use to find out a similar answer to a 5*5 square, without using a computer simulation?
If computer simulations are to be used, how would one go about solving this, and what is the principle involved in this kind of simulation?