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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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Answer Posted / rams
The answer is 31. All the perfect squares are on. ie 1,4,9,16,25,36....961(31*31).
Here is the logic.
The first person switches on every thing.
The multiple factors come in pairs, so the changes done by multiple factors has no effect. So all the Switches are on.
The switches are turned off by the person with same number.
The square root switches on the lights for the perfect squares.
| Is This Answer Correct ? | 9 Yes | 0 No |
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