The Locker Problem: Which Locker is Open?

The algorithm to solve the locker problem can be implemented using a simple program in Java. Here's the solution code:

Solution:

public class NewMain {
public static void main(String[] args) {
boolean[] locker = new boolean[101];
// Set all lockers to false (closed) initially
for (int i = 1; i < locker.length; i++) {
locker[i] = false;
}
// First student opens all lockers
for (int i = 1; i < locker.length; i++) {
locker[i] = true;
}
// Follow the students' rules to toggle the lockers
for (int S = 2; S < locker.length; S++) {
for (int k = S; k < locker.length; k += S) {
if (locker[k] == false) {
locker[k] = true;
} else {
locker[k] = false;
}
}
}
// Output the open lockers
for (int S = 1; S < locker.length; S++) {
if (locker[S] == true) {
System.out.println("Locker " + S + " Open");
}
}
}
}

This Java program follows the described algorithm where each student toggles the state of specific lockers. After all 100 students have passed through and changed the lockers, the program outputs the lockers that remain open. By running this program, you can determine which lockers are open based on the given rules.