math help ( its pretty hard)?

Question

if theres 1000 students at one school, and theres 1000 lockers..

the 1st student opened every locker,
the 2nd student closed every 2nd locker
the 3rd changed ( changed meaning opening closed ones, or closing opened ones) every third locker.
the 4th changed every fourth locker.


After all 1000 students had gone, which lockers were open?

Answer 1

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

In other words all the perfect squares less than a 1000

Answer 2

Ok, lets take the scale down to a simple 20
(O's stand for open, C's stand for closed)

1) O O O O O O O O O O O O O O O O O O O O
2) O C O C O C O C O C O C O C O C O C O C
3) O C C C O O O C C C O O O C C C O O O C
4) O C C O O O O O C C O C O C C O O O O O

As we can see, 13/20 remain open which is equivalent to 650/1000 or (650) lockers remain open

Since 1000 is and 20 is evenly divisible by 4 it means that the cycle was repeated 250 times completely so the answer is correct.

EDIT
Ok I was wrong I wrote a computer program to simulate this and come up with the numbers 583 open and 417 closed.
Edit
Ithink I misread your question, I thought that each student started at locker # 1 not the locker of that student, if the problem stated that they started at thier locker than the people who answered all squares up to 31^2 are correct.

Answer 3

There will be 31 locker doors open. The open doors correlate to the perfect squares that occur between 1 and 1000.

1^2 = 1 ==> door 1 open
2^2 = 4 ==> door 4 open
3^2 = 9 ==> door 9 open

The square root of 1000 = 31.62278 so therefore the last door that will be open will be number 961.

31^2 = 961

Doors 962 through 1000 will all be closed.

Answer 4

To repeat the person before me I think, its one locker. All the others get closed.

Answer 5

only the first one

this was not a hard question

Answer 6

poop thats confusing,, i'll get back to u on that

Answer 7

none