There are 1,000 (one thousand) lamps numbered from 1 to 1,000, which are all turned off.
There are 1,000 (one thousand) people numbered from 1 to 1,000.
The first person goes and turns on all the lamps.
The second goes to the even numbers of lamps (2, 4, 6…) and turns them off.
The third goes to the lamps which are multiples of 3 (3, 6, 9…) and turns on the "off" lamps or turns off the "on" lamps.
The fourth goes to the lamps which are multiples of 4 (4, 8, 12…) and turns on the "off" lamps or turns off the "on" lamps.
This continues up to the 1,000th person.
The 1,000th person goes to the 1,000th lamp, and turns it on if it is "off" or turns it off if it is "on."
How many lamps are "on" after all people finish their jobs?