title: locker puzzle using a boolean array
body: <p>I don't want the answer I want to know what I a doing wrong. below is the question</p>
  <p>A school has 100 lockers and 100 students. All lockers are closed on the first day of school. As the students enter, the first student, denoted S1, opens every locker. Then the second student, S2, begins with the second locker, denoted L2, and closes every other locker. Student S3 begins with the third locker and changes every third locker (closes it if it was open, and opens it if it was closed). Student S4 begins with locker L4 and changes every fourth locker. Student S5 starts with L5 and changes every fifth locker, and so on until student S100 changes L100.</p>
  <p>After all the students have passed through the building and changed the lockers, which lockers are open? Write a program to find your answer. The program should display the answer</p>
  <p>and my code is</p>
  <pre><code>public class LockerPuzzle {
  
      public static void main(String[] args) {
         
          
          boolean[] lockers = new boolean[100];
  
          // first all the lockers are closed. false represents closed
          for (int i= 0; i&lt;lockers.length;i++){
              lockers[i]= false;
              System.out.println(lockers[i]);
          }
  
          // then the first student comme and opens all the lockers
          for (int i = 0; i&lt; lockers.length; i++){
             lockers[i] = true;
          }
  
         
          int locker = 0;
          for(int j = 1; j&lt;= lockers.length; j++){
              for(int k =j; k&lt; lockers.length; k =k+j){
                  if(lockers[k] == false){
                      lockers[k]=true;
                  }else{
                      lockers[k]= true;
                  }
  
              }
          }
  
          // this prints all the open lockers.
          for(int S=0; S&lt;lockers.length; S++)
          {
              if (lockers[S] == true) {
                  System.out.println(&quot;Locker &quot; + S + &quot; Open&quot;);
              }
  
      }
    }
  }
  </code></pre>
  <p>and the output for me is saying all lockers are open.</p>