Question

Suppose there are 1000 lockers in a school hallway and they are all closed. Only 50 students

come through the hallway and start opening and closing the lockers. The first student opened all
the lockers. The second student closed every second locker and so forth. The Third student
changes the state of every 3rd locker. The fourth student changes the state of every 4th locker,
the fifth student changes the state of every 5th locker and so on, until the 50th student.
a. What is the state of the following locker numbers: #91, #1505, #625, #1000?
i. How do you know? (please show how you know)

Answer 1

Suppose there are 1000 lockers in a school hallway and they are all closed. Only 50 students

come through the hallway and start opening and closing the lockers. The first student opened all

the lockers. The second student closed every second locker and so forth. The Third student

changes the state of every 3rd locker. The fourth student changes the state of every 4th locker,

the fifth student changes the state of every 5th locker and so on, until the 50th student.

a. What is the state of the following locker numbers: #91, #1505, #625, #1000?

i. How do you know? (please show how you know)