The Mystery of the Open Lockers

Which lockers are open after all students have passed through the building?

The lockers that are open after all 100 students have passed through the building and changed the lockers are locker number 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.

To solve the mystery of the open lockers, we can follow the logic explained in the code provided. The code presents a Java program that simulates the process of students opening and closing lockers. Initially, all 100 lockers are closed.

As each student goes through the building and interacts with the lockers according to the specified rules, the program keeps track of which lockers are open. The program uses boolean values (true for open and false for closed) to represent the state of each locker.

The program utilizes nested loops to iterate through the lockers and simulate the actions of each student. The innermost loop checks whether a locker should be opened or closed based on the student's number. If a locker is closed, it is opened, and vice versa.

After all 100 students have completed their actions on the lockers, the program prints out the numbers of the lockers that are open. In this case, the lockers with numbers 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100 are found to be open.

This problem demonstrates an interesting pattern in the opening and closing of lockers based on the factors of the locker numbers. By running the provided Java program or understanding the logic behind it, you can uncover the solution to the mystery of the open lockers.