Open Doors

2022-10-17.py

question = """
Let's say you have n doors that start out as closed. With the 
first pass across the doors, you toggle every door open. With
the second pass, you toggle every second door. With the third, 
every third door, and so on. Write a function that takes in an 
integer numberOfPasses, and returns how many doors are open after 
the number of passes. Thanks Max for inspiring this question!

Example:

let n = 7
let numberOfPasses = 3

> passDoors(n, numberOfPasses)
> 4

// Explanation:
// 0 means open, 1 means closed
// Initial: 1 1 1 1 1 1 1
// Pass 1:  0 0 0 0 0 0 0
// Pass 2:  0 1 0 1 0 1 0
// Pass 3:  0 1 1 1 0 0 0

"""

def passDoors(doors, passes):
    doors_open = 0
    for door in range(1, doors+1):
        divisors = 0
        for i in range(1, passes+1):
            if (door / i) == int(door / i) and i <= passes:
                divisors += 1
        if divisors % 2 == 1:
            doors_open += 1
    print(doors_open)

doors = 7
numberOfPasses = 3

passDoors(doors, numberOfPasses)