1,000 lockers and 1000 Students Puzzle - Correct Answer?
There is a school with 1,000 students and 1,000 lockers. On the first day of term the headteacher asks the first student to go along and open every single locker, he asks the second to go to every second locker and close it, the third to go to every third locker and close it if it is open or open it if it is closed, the fourth to go to the fourth locker and so on. The process is completed with the thousandth student.
How many lockers are open at the end?
Ans : 31
the teacher makes to open only the perfect squares at the end.
31 is the perfect square below 1000.
1 2 3 4 5 6 7 8 9 10
1st o o o o o o o o o o
2nd o x o x o x o x o x
3rd o x x x o o o x x x
10th o x x o x x x x o x i.e., only perfect squares are open.