This is how the problem starts. All the cbana doors start out being closed. Student assigned to cabana 1 opens the doors on all 100 cabanas. The students assigned to cabana #2then closes doors on all cabanas whose numbers are multiples of 2. Th e student assisgned to cabana #3 then changes the state of all cabanas whose numbers are multiples of 3 ex: the door on cabana #3 which is open gets closed, and cabana #6 which is closed get opened. Come up wit some sort of system to simulate the opening and closing of the doors

Ah, a restatement of the locker problem.

While not stated in your original problem, I presume you have 100 students, not just 3.

At the end of the day, the open doors will be those numbers that have an odd number of factors. These will only be numers that are perfect squares. (1,4,9,...). All other doors will be closed.

To simulate the opening and closing of the doors, you can use a loop to go through each student and make the appropriate changes to the state of the doors. Here's an example in Python:

```python
# Initialize a list of 100 doors, all closed
doors = [False] * 100

# Iterate over each student from 1 to 100
for student in range(1, 101):
# Iterate over each door based on the student's number
for door in range(student, 101, student):
# Change the state of the door
doors[door - 1] = not doors[door - 1]

# Print the result
for i, door_state in enumerate(doors):
door_number = i + 1
if door_state:
print("Door #{} is open.".format(door_number))
else:
print("Door #{} is closed.".format(door_number))
```

This simulation follows the exact steps described in the problem statement. The outer loop represents each student, and the inner loop goes through the doors to be affected by that student. The `door - 1` index adjusts for the fact that the door numbers are 1-indexed while list indices are 0-indexed.

After the simulation finishes, it will print the state of all 100 doors, indicating which doors are open and which ones are closed.