ClaytonW
Level: Smitemaster
Rank Points: 961
Registered: 02042003
IP: Logged

Re: Puzzle "tag" (0)
First I'll laugh at myself for attempting to solve this by repeatedly filling in 1000 little bubbles in MSPaint. Secondly, I'll admit I still used that wonderful Windows tool to solve this.
I made 20 circles instead of 1000, and went through 20 loops of the puzzle. Once student "n" goes through, the state of locker "n" is never altered again. At the end of 20 iterations, the lockers that are still open are 1, 4, 9, and 16. I recognized those numbers immediately as being perfect squares. So, the number of open lockers at the end of the Principal's cruel, cruel, game is equal to the number of perfect squares within the 11000 range. The largest perfect square under 1000 is 961. And the square root of that means...
31 lockers were still open.
(The perfect squares are ~courtesy of TI89~: 1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289,324,361,400,441,484,529,576,625,676,729,784,841,900,961)
