**Problem Three** **An Open And Shut Case**
In a particular corridor of a school there are 25 lockers numbered from 1 to 25.

At recess, a class of 25 students decided to try an experiment.

Each student is to walk along the corridor one at a time.

- The first student will open all of the locker doors.
- The second student will close all of the locker doors with even numbers.
- The third will change all the locker doors with numbers that are multiples of three. This means to close any open doors and open any closed doors.
- The fourth will change all the locker doors with numbers that are multiples of four and so on.

- Which locker doors will be left open after the tenth student has passed through the corridor? Explain.
- Which locker doors will be left open after 25 students have all passed through the corridor? Explain.
- If there were 1000 students are 1000 lockers which locker doors will now be left open? Explain.