While I am thinking about it...

I've been going though my "protector file" (so named because it consists of hard-to-categorize items stored in page protectors) a little at a time, as a kind of warmup to work - and to cut down on the size of the file somewhat, and ran across the following classic:

Three salesmen register at a hotel and pay $10 each for separate rooms. After they've gone upstairs, the manager realizes they've been overcharged a total of $5, so he sends the bellhop upstairs with instructions to return the money to the salesmen. On the way up, the bellhop decides to pocket $2 for himself, and returns only $1 to each salesman.

Now here's the situation: each salesman has paid $9 for his room, which amounts to $27. Add the $2 in the bellhop's pocket, and that's $29. What happened to the other dollar?

The typed explanation in my file is long-winded, but as I looked it over, I noticed I could streamline it quite a bit.

But I haven't the time to set it down right now.

In the meantime, I'd be interested in reading your solutions!

UPDATE:

My explanation starts with observing that, as far as each salesman is concerned, each believes he has paid $9 for a room. That $9, plus the $1 returned by the bellhop accounts for all of the $30 that initially changed hands. The $2 in the bellhop's pocket is a distraction, representing the difference between the $27 paid by the three salesmen and the $25 charged for lodging by the hotel.

Like LJ friend rjlippincott, I too, used to wonder about how three people can end up with a total $5 refund (and even more, why send a bellhop with five ones, since that really doesn't solve the problem), until I read LJ friend skipperja's version of the story, which would at least make the setup more believable.

Indeed, the catch in this apparent "paradox" is thinking that what the three men "paid" plus what the bellhop held back must amount to the $30 that initially changed hands. If you ignore the three $1 refunds it's an easy conclusion to be led to.

Cheers....