The big Switch-eroo Mathematics

in /by

The big Switch-eroo Mathematics

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?

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