Question

There are 1000 lockers, all shut and unlocked, and 1000 students.

Suppose the first student goes along and opens every locker.
The second student goes along and shuts every other locker beginning with number 2.
The third student then goes along and changes the state of every third locker beginning with number 3. (If the locker is open, the student shuts it and if the locker is closed, the student opens it.)
The fourth student changes the state of every fourth locker beginning with number 4.
If this continues until all 1000 students have followed the pattern with these lockers, which lockers will be open and which will be shut at the end? Why?

Answer 1

if i remember it is the number of squares

Answer 2

up to 1000

Answer 3

therefore it is 4, 9, 16,25, 36, etc

Answer 4

do you get it @smourin ??

Answer 5

can you explain it?

Answer 6

well if you calculate up to the 4th student...you'll see that the 4th student opened the 4th door

Answer 7

the 5th onwards will not touch this opened door

Answer 8

From the 4th person onwards till the 10th person is open, close, close, open, open, open, open, open, close, close, right?

Answer 9

sorry i had to step out...

Answer 10

anyway...as i was saying...

Answer 11

1 opens all doors
2 starts at 2nd door that means 1st door remains open from 2nd student onwards

Answer 12

2 closes 2nd door, 4th door, 8th door, etc.