The Locker Problem

The Locker Problem
Leo Troast
10/02/09
The pattern for the problem is Open, Closed, Closed, Open, Closed, Closed, Closed, Closed, Open, Closed, Closed, Closed, Closed, Closed, Closed, Open. It is this because only the perfect squares are open, this is because it has an odd amount of factors Ex – 16 (Perfect square) Factors = 1, 2, 4, 8, 16 compared to 18 (imperfect square) Factors = 1, 2, 3, 6, 9, 18. this means that for a perfect square an odd amount of numbers go into it so that means it will be (referring to 16) opened then closed, opened, closed, then opened again. They will stay open because once that last factor comes through to open it then the numbers will have gotten bigger then it so it wont be touched. 31 out of the 1000 are open because there are 31 perfect squares from 1-1000. 969 are closed because those are all the numbers that are not perfect squares from 1-1000.