There are 1,200 refrigerators numbered 1 to 1,200. Suppose you open all of the refrigerators and then close every other refrigerator. Then, for every third refrigerator, you close each opened refrigerator and open each closed refrigerator. You follow the same pattern for every fourth refrigerator, every fifth refrigerator, and so on up to every twelve hundredth refrigerator. Which refrigerators will be open when the process is complete? Describe the mathematics that is underlying this math problem in your answer.