1000student has individual locker. First student opens all lockers and second student closes all even number of lockers . Similarly 3rd students goes to 3rd number of locker like 3 6 9 12 upto 999. similarly forth goes to 4 table number like 4 8 12 16 up to 1000. thus all 1000 students go to their respectively lockers and they open all if they find closeotherwise they close if they find open. So you have to tell that afterlast student how many lockers will open.

• ans: 31
  for perfect squares the no of factors is odd and the locker numbers with odd factors will be open. Others will be closed. There are 31 perfect squares from 1 to 1000.
• 10 years agoHelpfull: Yes(2) No(0)
• answer is 1000-31=969
  
  this question is based on the concept of factors
  we know that for finding factor of any number,we use following logic
  number = a^p * b^q
  so number of factor=(p+1)(q+1)
  
  here from 1 to 1000 there are 31 perfect squares,and for perfect square, number of factors are odd and if number of fcators are odd than locker is in close condition and if number of factors even than locker is in open condition.
  
• 10 years agoHelpfull: Yes(1) No(1)