/* A school has 100 students and 100 lockers.  Student 1 opens all 100 lockers.  Student 2, beginning with the
 * second locker, closes every other locker.  Student 3, starting with locker 3, changes every 3rd locker (opens
 * any closed locker, closes any open locker).  Student 4, starting with locker 4, changes every 4th locker, etc.
 * When done, which lockers are open and which are closed?
 *
 * Here, we use lockers 0..99 and students 1..100 but student i is going to start at locker i-1.  We use true for
 * open and false for closed */

public class Prog7_23
{
	public static void main(String[] args)
	{
		boolean[] lockers = new boolean[100];
		for(int i=0;i<100;i++) lockers[i] = true;			// student 1 opens all lockers to start
		for(int student=2;student<=100;student++)			// students 2-100 take turns
			for(int locker=student-1;locker<100;locker=locker+student)		// for each locker, notice we start at student-1 since lockers are actually 0-99
				if(lockers[locker]) lockers[locker]=false;	// change lockers[locker] (open if closed, close if opened)
					else lockers[locker] = true;
		for(int i=0;i<100;i++)								// output the results
			System.out.println((i+1) + " " + lockers[i]);
			
	}
}