A school$$s lockers are numbered $1$ to $100.$ One hundred students

enter the school one at a time. The first student opens the lockers.

The second student closes the even numbered lockers. The third

student either closes or opens every third locker. The remaining

students continue the pattern. Write a program to determine

which lockers remain open at the end, after the last one of the

students passes. Explain the result. Make sure the program not

only reports the situation at the end but also conveys the stages

through which the array of lockers passes.