Imagine you are at a school that still has student lockers.  There are
1000 lockers, all shut and unlocked, and 1000 students.
(1) Suppose the first student goes along the row and opens every locker.
(2) The second student then goes along and shusts every other locker
beginning with number 2.
(3) The third student changes the state of every third locker
beginning with number 3.  (If the locker is open the student shuts it,
and if the locker is closed the student opens it.
(4) The fourth student changes the state of every fourth locker
beginning with number 4.  Imagine that this continues until the
thousand students have followed the pattern with the thousand lockers.
 At the end, which lockers will be open and which will be closed? 
Why?

This previous question may interest you:
http://answers.google.com/answers/threadview?id=469968

I assume u mean that the 101th person onwards will only close his/her
own locker and so the link is useless.

---
Answer:
Doors open: 1, 20-199
Doors closed: 2-19,200-1000

---
Working:

Consider the doors in sets: 1, 2-9,10-19,20-99,100-199,200-999,1000
Door 1 is opened by 1st person so remains open.
Doors 2-9 are opened by person 1, then closed by persons 2-9 respectively.
Doors 10-19 are opened by person 1, then closed by persons 10-19 respectively.
Doors 20-99 are opened by person 1, closed by persons 2-9, then opened
by persons 20-99.
Doors 100-199 are opened by person 1, closed by persons 10-19, then
opened by persons 100-199.
Doors 200-999 are opened by person 1, closed by persons 2-9, then
opened by persons 20-99 and closed by persons 200-999.
Door 1000 is opened by person 1, closed by person 10, opened by person
100 and closed by person 1000.

1. Lockers with prime numbers will be touched exactly twice.  By
Person #1 and person N.  The two factors of N.
2. Lockers with numbers that have an even number of factors will be
touched an even number of times.
3. Lockers with an odd number of factors will be touched an odd number of times.

OK, so what numbers have an odd number of factors?  Only squares.

When done, only the lockers whose numbers are square numbers will be
open.  All others will be closed.
Open lockers will be 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, etc.

Gee2,

Well done!