# Puzzles & Games 1000 lockers problem -solved by Icewolf

Discussion in 'Puzzles & Games' started by helenheaven, Nov 24, 2004.

1. ### helenheavenPremium Member

There are 1000 lockers in a high school with 1000 students. The
problem begins with the first student opening all 1000 lockers; next
the second student closes lockers 2,4,6,8,10 and so on to locker 1000;
the third student changes the state (opens lockers closed, closes
lockers open) on lockers 3,6,9,12,15 and so on; the fourth student
changes the state of lockers 4,8,12,16 and so on. This goes on until
every student has had a turn.

How many lockers will be open at the end? What is the formula?

2. ### smilingsarah82Member

i just want to say that i have been trying to develop a pattern for this one, and my brain now hurts, so i am going to leave it alone for now, and come back to it later.......

3. ### IcewolfPremium Member

This one was quite simple, but I love numbers, the answer to this problem is that the lockers which have an odd number of divisors will be open. i.e. square numbers and there are 31 square numbers up to 1000, so I'd say 31 lockers are left open.