you have to tell how many windows will be opened if initially there are 1000 open windows are there and there are 1000 students.
and every student is going to close/open (if open than close it and vice versa) the window that lies on its factor
suppose student with no 1 goes than it will close all the initially open windows and after it student2 goes & it will open/close (in this case it will open)the windows on its factor like 2,4,6,8,10,...1000
similarly now student3 goes and open/close windows(in this case it will open those windows that are at factor of 3 and close that window that have lcm(2,3)i.e. window at 6,12 )
so all you have to tell how many windows there be close at the end when 1000 student have done his part
remember the student 1000 have only to go on 1 window numbered 1000 that is it is the only factor
and also tell the number of the window that will be closed

• @kavita: no of perfect squares below 1000 is 31 not 33
• 12 years agoHelpfull: Yes(2) No(0)
• Here the numbers with even factors will be open and rest will be closed. as 2nd person will open the window.. now we find out the numbers from 1 to 1000 with odd factors. that are numbers with perfect square lying below 1000 ie 33. so number of windows that are closed are 1000-33 = 967
• 12 years agoHelpfull: Yes(1) No(2)