Where Did the Other Dollar Go? - A Classic Tale

[Rahmuss]

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?

 

[chroot]

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

 

[Huckleberry]

This one has been done on this site before.
https://www.physicsforums.com/showthread.php?p=540199#post540199