And now for something completely different...

This blog usually contains reflections on personal prayer. However, during this Christmas season, I want to do something completely different for this entry. I'm posting a puzzle.

For the last few years, we have included a Christmas puzzle with our family's Christmas newsletter. In this year's newsletter, I included the URL for this blog and asked our newsletter recipients to see the new blog. So, in this entry, I'm including a bonus Christmas puzzle (to try to make up for last year's newsletter, which, due to time commitments, never got sent out in time.

So, for family, friends and readers of this blog, the bonus puzzle follows:

Santa's 1000 elves each have their own individual locker. These lockers are found one next to each other in a very long corridor of Santa's workshop. All the lockers start out being closed. Elf #1 opens every locker. Elf#2 closes every second locker(i.e. Lockers 2,4,6,8,10,etc). Elf #3 changes the state of every third locker (i.e. if opened, he closes it; If it is closed, he opens it). Elf #4 changes the state of every fourth locker. Elf #5 changes the state of every fifth locker. Each following elf does the same (i.e. Elf "n" changes the state of every "n"th locker).

After Elf 1000 changes the state of Locker 1000, which lockers are open?

Please feel free to post your answers via the Comments. I will have the answer on the Christmas Day entry to this blog. Have fun with the puzzle. Merry Christmas!!!