How many doors are open

There are 1 500 people crowded in a large room. Connected to the room is a long hallway containing 1 500 closed doors. The first person in the room begins by opening every door in the long hallway. The second person goes and closes every other door. The third person goes to every third door and opens it if it is closed and closes it if it is opened. The fourth person goes to every fourth door and does the same procedure and so on. How many doors are left open after the 1 500th person has completed this cycle?

[James Tursa]

What have you done so far? What specific problems are you having with your code? What is your specific MATLAB question?

[Phakiso Mason]

This is what I have done so far. The code is not running.

x = 1500;

y_correct = [1, 4, 9, 16, 25,36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444];

assert(isequal(square(x),y_correct))

[Ntombikayise Bhengu]

Thank you so much. It unfortunatey it didnt run.

Answer 1

[David Hill]

doors=zeros(1,1500);
for k=2:1500
    doors(k:k:1500)=~doors(k:k:1500);
end
open=nnz(doors==0);

[Ntombikayise Bhengu]

Thank you so much.

[Stephen23]

Without multiple implicit data type conversions:

doors = false(1,1500); % open=true
for k = 1:1500
    doors(k:k:1500) = ~doors(k:k:1500);
end
open = nnz(doors);