PLEASE HELP

BRAINLIEST WILL BE WHOEVER GIVE ME THE CORRECT ANSWER WITH EXPLANATION!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

A hotel has 100 rooms, numbered 1-100, and each room has a blue door. The manager decides the doors need new paint, so she has them all painted red.


Then the manager decides that she would like every 2nd door painted blue, beginning with door number 2. So the painter dutifully paints every 2nd door blue.


Next, the manager decides that beginning with door 3, to mix things up, she wants the painter to change the current color of every 3rd door; so if the door is red, paint it blue, and if it’s blue, paint it red. So the painter orders more paint and gets to work.


What next? You guessed it! The manager wants every 4th door to have its color changed, beginning with door number 4. Then she wants every 5th door’s color changed, beginning with door number 5, then every 6th door changed, … and so on to the 100th door!