/*
 * There are one hundred closed lockers in a hallway.
 * A man begins by opening all one hundred lockers.
 * Next, he closes every second locker.
 * Then he goes to every third locker and closes it if it is open or opens it if it is closed
 * (e.g., he toggles every third locker).
 * After his one hundredth pass in the hallway, in which he toggles only locker number one hundred,
 * how many lockers are open?
 */
/*
* Below same solution can be applied for the switches question also.
*/
public class Doors {
 public static void main(String[] args) {
  int doorsN = 1000;
  boolean[] doors = new boolean[doorsN];
  for(int i = 0; i < doorsN; i++) {
   doors[i] = false;
  }
  int round = 1;
  while(round <= doorsN) {
   for(int i = 0; i < doorsN; i++) {
    if((i+1)%round == 0) {
     if(doors[i])
      doors[i] = false;
     else
      doors[i] = true;
    }
   }
   round++;
  }
  for(int i = 0; i < doorsN; i++) {
   if(doors[i]) {
    System.out.println(i+1);
   }
  }
 }
}

Much faster way:-
public class Doors {
    public static void main(String[] args) {
         int doorsN = 1000;
         int round = 0;
         while((++round)*round <= doorsN)
              System.out.println(round*round);
     }
}