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Math Help - trickey one !!!

  1. #1
    Junior Member
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    trickey one !!!

    The warden meets with 23 new prisoners when they arrive. He tells
    them, "You may meet today and plan a strategy. But after today, you
    will be in isolated cells and will have no communication with one
    another.

    "In the prison is a switch room, which contains two light switches
    labeled A and B, each of which can be in either the 'on' or the 'off'
    position. I am not telling you their present positions. The switches
    are not connected to anything.

    "After today, from time to time whenever I feel so inclined, I will
    select one prisoner at random and escort him to the switch room. This
    prisoner will select one of the two switches and reverse its position.
    He must move one, but only one of the switches. He can't move both but
    he can't move none either. Then he'll be led back to his cell.

    "No one else will enter the switch room until I lead the next prisoner
    there, and he'll be instructed to do the same thing. I'm going to
    choose prisoners at random. I may choose the same guy three times in a
    row, or I may jump around and come back.

    "But, given enough time, everyone will eventually visit the switch
    room as many times as everyone else. At any time anyone of you may
    declare to me, 'We have all visited the switch room.' and be 100%
    sure.

    "If it is true, then you will all be set free. If it is false, and
    somebody has not yet visited the switch room, you will be fed to the
    alligators."

    What is the strategy they come up with so that they can be free?
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  2. #2
    Super Member Deadstar's Avatar
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    Its something along the lines of...
    One guy is the counter.
    He switches the light off whenever it is on.
    Everyone else turns it on ONCE unless it is already on in which case they leave it. (i.e. if they have already come into the room and turned the light on earlier then they dont turn it on again)
    Once the counter has turned the light off 23 times he knows everyone has turned it...

    Just typed that then re-read the question to realize that's not really the right answer...

    Something along those lines...

    What do the switches A and B do? Does one turn it off and one turn it on? Do they both turn it off and on? Is there two lights..?

    Modify my answer somehow and I imagine it'll work...
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  3. #3
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    may be answer but not

    The group of prisoners here will have to choose a leader among
    themselves.So barring him there are 22 other persons.The leader will
    be the person who will flip the first switch "DOWN".The other 22
    members will flip that switch "UP" two times each.So when the leader
    counts that he has flipped that switch "DOWN" 44 times, he will tell
    the warden that they have all visited the dungeon and be freed.

    but few flaws here

    1. say the warden decides to send each only once inside the switch box
    & the last or the first man is the leader then your solution would not
    address this probem.
    2.say everyone other than the leader visits the box twice and at last
    the leader is sent in to the switches room twice
    the same day then his count would still only be zero !

    The last one to be conquered will be death !
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  4. #4
    Super Member Deadstar's Avatar
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    Every prisoner takes a shoe off and throws it in the corner.
    Count the shoes.
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  5. #5
    Senior Member
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    Quote Originally Posted by Deadstar View Post
    Every prisoner takes a shoe off and throws it in the corner.
    Count the shoes.
    BRILLIANT !!!
    LOL !!!!
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  6. #6
    MHF Contributor
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    Quote Originally Posted by bluffmaster.roy.007 View Post
    "But, given enough time, everyone will eventually visit the switch
    room as many times as everyone else.
    What if their jail sentence (say 5 years) ends before all the prisoners
    have visited at least once?
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