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Math Help - Logic riddle

  1. #1
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    Logic riddle

    There are ten columns arranged horizontally, and an invisible man jumping above them, one random jump to the left or to the right, from column to column.
    Our goal is to shoot this invisible man with a rifle.
    What is the minimal number of shots required to guarantee that we will hit him?

    Thanks for any help...
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  2. #2
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    Re: Logic riddle

    Ah, a problem statement from the 1950s before we were all sensitive about that sort of thing.

    P(first hit) = 1/10?
    P(2nd hit) = (9/10)(1/10)
    P(3rd hit) = [(9/10)^2](1/10)
    ...

    Why is there a guarantee?

    Is the edge behavior important? If he is far right, he can't go farther right, but then it's not random. Hmmm... I've begun to be suspicious since now, if he's on #9, he must go to #8, since we've established that he can't go to #10. That's not random, either. Now we have a different problem, since he can't go to #1, #2, #9, or #10

    P(first hit) = 1/6?
    P(2nd hit) = (5/6)(1/6)
    P(3rd hit) = [(5/6)^2](1/6)
    ...

    Why is there a guarantee?

    Hmmm... More thinking. Your turn.
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  3. #3
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    Re: Logic riddle

    what i thought was, shoot at the second to the left-most column (can we just call this #2?), twice.

    then we know for sure he's not at #1 or #2 (unless we hit him already, and he's dead. departed. kaput. swimming with the fishes.)

    so we move to #3. now it might be the case that he was just on #3, and jumped left. so we shoot again (if he was on #2 and jumped back, this will get him).

    but, maybe we miss again (even with our super-duper laser scope). well, he's not on #3, and he wasn't on #2, so he's either on #2 (he has to jump there

    from #1), or he's on #4 or higher. so shoot at #2. if we miss, after his jump he has to be on #3 or higher. so we shoot at #3. if we miss yet again,

    that means he wasn't on #4 and jumped to #3, so he must have jumped even higher (to #5 or more). so now we can safely move to #4....
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    Re: Logic riddle

    Quote Originally Posted by CaramelCardinal View Post
    That's only clearly the answer if you can fire all of the shots at once (consider a version of this where the man can jump from 10 to 1 or 1 to 10, in which case you cannot guarantee you will ever hit him). I think Deveno is correct...I was thinking the same algorithm, but it didn't dawn on me at first that I could start from the second column.

    How you end the hunt is also a critical piece of the algorithm. I won't say whether or not it happens to match up with pigeonhole, though...
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  6. #6
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    Re: Logic riddle

    I can hit him in 1 shot.
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    Re: Logic riddle

    Oh, that's awesome. Bravo.

    You do have to make an assumption about what one of the words in the problem means in order for that to work, though, since I don't think it's quite specific enough (it needs to be exact about the relationships). But I think you may be right with the IS.
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    Re: Logic riddle

    Quote Originally Posted by Annatala View Post
    Oh, that's awesome. Bravo.

    You do have to make an assumption about what one of the words in the problem means in order for that to work, though, since I don't think it's quite specific enough (it needs to be exact about the relationships). But I think you may be right with the IS.
    I hope you find this post amusing.

    As a great man once said, "it all depends on what your definition of IS, is"

    Maybe to that we can add, "we must be very cautious of what our assumptions about ARE, are"

    Anyway, Gödel wins again.



    I was thinking of lining up the columns, then 1 shot takes him out, but i like your observation about IS.
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    Re: Logic riddle

    Quote Originally Posted by agentmulder View Post
    As a great man once said, "it all depends on what your definition of IS, is"
    Sorry! Intended Solution. It's a common abbreviation in another forum. :P
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    Re: Logic riddle

    Quote Originally Posted by Annatala View Post
    Sorry! Intended Solution. It's a common abbreviation in another forum. :P
    Right now i am grinning from ear to ear after reading your post.


    Since 'is' is not the word you mentioned, what is the word?

    I thought you implied that since the goal is to shoot him, you only need 1 shot.

    I'm curious as to what is the word.
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    Re: Logic riddle

    Quote Originally Posted by agentmulder View Post
    Since 'is' is not the word you mentioned, what is the word?
    "Horizontally." Taken literally, this suggests all columns are at the same height (the tops are aligned with the axis of the horizon), and since it is from the perspective of the shooter it also suggests that they are arranged in order from left to right (so no two columns obscure one another). However, it does not require they are lined up in parallel (imagine that they could be arranged in a semicircle, for example). If it said "columns of equal height, arranged in a straight row horizontally" this would eliminate the ambiguity.
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  12. #12
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    Re: Logic riddle

    If the man is (oops!) invisible, how would you know if you hit him or not?

    If you circle around and line up the columns then 1 shot gaurantees a hit because we know he has to be on a column when you take the shot.

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    Re: Logic riddle

    Quote Originally Posted by agentmulder View Post
    If the man is (oops!) invisible, how would you know if you hit him or not?
    Mainly the screaming (or the loud "ding!" sound if you have that useful TF2 mod set).

    ...or the sound of invisible blood splatting against the ground.

    ...or the odor (this may take a few days, though).
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    Re: Logic riddle

    Quote Originally Posted by Annatala View Post
    Mainly the screaming (or the loud "ding!" sound if you have that useful TF2 mod set).

    ...or the sound of invisible blood splatting against the ground.

    ...or the odor (this may take a few days, though).
    If I was the invisible man i would scream after you took the 1st shot whether you hit me or not. This would make you stop shooting.

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    Re: Logic riddle

    Quote Originally Posted by agentmulder View Post
    If I was the invisible man i would scream after you took the 1st shot whether you hit me or not. This would make you stop shooting.
    He'd better be a good actor!

    I suppose I could always hire Benedict of Amber to do it for me. He would be able to guess correctly based solely on the man's most likely strategy...
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