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Math Help - 3 guys go to a Hotel

  1. #1
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    3 guys go to a Hotel

    i was asked this puzzle today
    three guys go to a hotel the man there says its 30$ a nite so they each give him 10$
    then the man comes back to them and says i made a mistake its 25$ a night he gives each of them 1$ back and says i can't make change for the last 2$ so they each payed 9$ 3x9 is 27 plus the 2 the man kept is 29 where is the other dollar to make 30$ and or way does the math work one way and not this way
    i know there is something i don't get or do not know of so take it ez on im an old guy
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  2. #2
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    If x=\sqrt{2} then x\not= \pi.
    That is the nonsense of this question.
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  3. #3
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    One of the silliest/oldest puzzle; google "Missing dollar riddle".
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  4. #4
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    Quote Originally Posted by toren View Post
    i was asked this puzzle today
    three guys go to a hotel the man there says its 30$ a nite so they each give him 10$
    then the man comes back to them and says i made a mistake its 25$ a night he gives each of them 1$ back and says i can't make change for the last 2$ so they each payed 9$ 3x9 is 27 plus the 2 the man kept is 29 where is the other dollar to make 30$ and or way does the math work one way and not this way
    i know there is something i don't get or do not know of so take it ez on im an old guy
    I have heard this puzzle before but thinking about it right now the $2 which we add is included in the $9 spent by the three person and it does not fit with the remainder of the $10. The puzzle by itself misleading us to add the $2 from which it is made out off.
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  5. #5
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    Quote Originally Posted by sgguhan View Post
    The puzzle by itself misleading ......
    Well, if it wasn't misleading, then it wouldn't be a "puzzle", right?
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    Quote Originally Posted by Plato View Post
    If x=\sqrt{2} then x\not= \pi.
    That is the nonsense of this question.
    Haha, indeed. I like the confusion it creates, though.
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  7. #7
    Member agentmulder's Avatar
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    Re: 3 guys go to a Hotel

    How come nobody is adding the dollar each man has in his pocket?

    Each man paid 9, the bellhop has 2, each man has a dollar, total... 32 dollars!



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  8. #8
    Junior Member mathbyte's Avatar
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    Post Re: 3 guys go to a Hotel

    OK, I'll be a bit serious... no, it's not easy for me

    As others have said, this is a pretty famous problem, and you may well have already Googled the solution. The answer is that the numbers are added incorrectly.
    But the numbers are fine. Consider: when all is said and done, the room is $25. They tipped the bellhop $2. $25 plus $2 is the $27 total paid, or $9 per man.

    Suppose the bellhop had made a really big error and said the room is $16 per night, not $30. Okay, so he gives each man $4 back, and says I cannot make change for the $2 i have left. They let him keep it.
    Using these numbers, the problem would have been worded something like:
    "So each man paid $6. $6x3 is $18 plus the $2 the bellhop kept, which is $20. Where is the missing $10 to make $30?"
    ...and that question will likely be pondered far less. A much bigger error causes one to consider sooner that something is amiss.

    The problem has stuck since the "difference" using this funny reasoning and the numbers it does is only $1. When it gets bigger than that, as it just did when we used different numbers, the faulty addition is easier to see...
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  9. #9
    Member agentmulder's Avatar
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    Re: 3 guys go to a Hotel

    Quote Originally Posted by mathbyte View Post
    OK, I'll be a bit serious... no, it's not easy for me

    As others have said, this is a pretty famous problem, and you may well have already Googled the solution. The answer is that the numbers are added incorrectly.
    But the numbers are fine. Consider: when all is said and done, the room is $25. They tipped the bellhop $2. $25 plus $2 is the $27 total paid, or $9 per man.

    Suppose the bellhop had made a really big error and said the room is $16 per night, not $30. Okay, so he gives each man $4 back, and says I cannot make change for the $2 i have left. They let him keep it.
    Using these numbers, the problem would have been worded something like:
    "So each man paid $6. $6x3 is $18 plus the $2 the bellhop kept, which is $20. Where is the missing $10 to make $30?"
    ...and that question will likely be pondered far less. A much bigger error causes one to consider sooner that something is amiss.

    The problem has stuck since the "difference" using this funny reasoning and the numbers it does is only $1. When it gets bigger than that, as it just did when we used different numbers, the faulty addition is easier to see...
    Yeah, but each man has $4 in his pocket... making the total $32...AGAIN!

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  10. #10
    Junior Member mathbyte's Avatar
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    Red face Re: 3 guys go to a Hotel

    Quote Originally Posted by agentmulder View Post
    Yeah, but each man has $4 in his pocket... making the total $32...AGAIN!

    Sure... "that" way of adding it will always be $32. $30 plus $2 is always $32. If one starts running the numbers:

    $30 paid, $1 each given back from the bellhop:
    $9 each plus $1 each in their pocket plus $2 to the bellhop: = 27+3+2 =32

    $30 paid, $2 each given back from the bellhop:
    $8 each plus $2 each in their pocket plus $2 to the bellhop: = 24+6+2 =32

    $30 paid, $3 each given back from the bellhop:
    $7 each plus $3 each in their pocket plus $2 to the bellhop: = 21+9+2 =32

    $30 paid, $4 each given back from the bellhop:
    $6 each plus $4 each in their pocket plus $2 to the bellhop: = 18+12+2 =32

    and so on.

    In other words, where

    r=room rate
    c=change given back

    you're adding:

    3*r + 3*c +2

    3*(r+c) +2

    But, r+c is always 10. Thus,

    3*(10)+2 = 32.

    Still, that's what a to-remain-nameless former U.S. President would call "Fuzzy Math."
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