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Missing Dollar

  1. May 12, 2005 #1
    I didn't see this one here. I took it from this site. It's a classic for those who haven't seen it yet.

    Three friends check into a motel for the night and the clerk tells them the bill is $30, payable in advance. So, they each pay the clerk $10 and go to their room. A few minutes later, the clerk realizes he has made an error and overcharged the trio by $5. He asks the bellhop to return $5 to the 3 friends who had just checked in. The bellhop sees this as an opportunity to make $2 as he reasons that the three friends would have a tough time dividing $5 evenly among them; so he decides to tell them that the clerk made a mistake of only $3, giving a dollar back to each of the friends. He pockets the leftover $2 and goes home for the day! Now, each of the three friends gets a dollar back, thus they each paid $9 for the room which is a total of $27 for the night. We know the bellhop pocketed $2 and adding that to the $27, you get $29, not $30 which was originally spent. Where did the other dollar go????
  2. jcsd
  3. May 12, 2005 #2


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    Staff Emeritus
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    Gold Member

    This riddle purposefully confuses negative and positive quantities.

    Before the refund, the manager had $30, the friends $0, and the bellhop also $0: total $30.

    After the refund, the manager had $25, the friends $1 each, and the bellhop $2: total $30.

    The next-to-last sentence of the riddle makes use of the fact that the friends paid a net $9 each to imply that the manager had $27 after the refund, when in fact he only had $25.

    - Warren
  4. May 12, 2005 #3
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