There is a room with 1000 light switches, numbered 1, 2, 3, 4, ... 1000, all turned off. Outside the room there are 1000 men, numbered man1, man2, ...man 1000 In order, each man walks into the room and changes the position of each switch that is a multiple of his number. That is: man1 flips every switch man2 flips switches 2, 4, 6, 8 ....1000 man3 flips switches 3, 6, 9, ..... 999 ..... Man 1000 flips switch 1000 After all 1000 men are done, how many switches are on?

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