[Psycho]

nope, 31 open and 969 closed, reason being is that the only way a locker can be open, is if it changed an odd amount of times, and the only time it changes is when the number is a multiple. The only numbers with even multiples are perfect squares, so the lockers that are open are 1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,25 6,289,324,361,400,441,484,529,576,625,676,729,784, 841,900,961

add em up, you get 31 open!

basically these numbers are 1^2, 2^2, 3^2,4^2...39^2 perfect squares