In a certain electrical company warehouse there were 2000 light switches lined up
along one wall and 2000 employees. At the end of each year, the employees would line
up and perform the following strange ritual: Before the
beginning of the ritual, all of the
switches were turned off. The first employee turned every light switch on. The second
employee went to every second switch and turned it off. The third employee went to
every third light switch and changed it (i.e., if the switch was on, the employee turned it
off; if it was off, the employee switched it on). In a similar way, the fourth, fifth, sixth,...
employee changed every fourth, fifth, sixth,... light switch. After all 2000 employees
had passed by the switches, which switches were on?