Design an algorithm to solve the locker doors problem

described in exercise $12,$ page $8.$ There are n lockers in a hallway, numbered sequentially from $1$ to n$.$

Initially, all the locker doors are closed. You make n passes by the lockers, each time starting with locker

#$1.$ On the ith pass, i $=1,2,...,$ n$,$ you toggle the door of every ith locker: if the door is closed, you open it;

if it is open, you close it$.$ After the last pass, which locker doors are open, and which are closed?