While I am thinking about it...

[alexpgp]

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....

Comments

[skipperja.livejournal.com]

It's a matter of adding up the wrong amounts and presenting the result as a solution.
Take the approach of adding up what was PAID and then what was RECEIVED and the results balance.
The three guys initially paid $30, but received $3 in a refund, so the total paid was $27 dollars.
The inn keeper received $30 initially, but gave $5 to the bellhop, so the inn keeper had $25.
The bellhop gave $3 to the guys, so he received $2.
The inn keeper and the bellhop received a total of $27 which balances the $27 that the three guys paid.

Our pastor once told several of us about this 'unsolvable' problem. When I told him the solution, he continued to insist that it could not be solved. I finally gave up. :P

Is that a short enough solution?

[ex-greymaide85.livejournal.com]

You beat me to it.

As far as I can tell, this is just a math problem to scare the crap out of sixth grade math students ;)

[astroprisoner.livejournal.com]

Yeah, the above solution pretty much covers it.

This sort of puzzle results from shifting mathematical gears between addition and subtraction in order to intentionally confuse the issue.

Here's a much simpler one: you can prove that people have eleven fingers. Hold out one hand and count the fingers "One two three four five," effectively adding them to zero. Now hold out your other hand, but this time count down, "Ten nine eight seven six" effectively subtracting them from ten.

Add five and six, you get eleven fingers.

(Stan the icon man is holding up the missing digit.)

Here's my question that no one seems to ask: how can three people be overcharged by the even amount of five dollars? That means each was overcharged by one dollar and 66.666666 cents.

Where did the extra fraction of a penny come from?

[skipperja.livejournal.com]

There are probably several versions of the story, but this is what I remember:
$10 was the cost of an individual room. However, there was only one room available. The three men agreed to share the room, but the clerk charged them the individual room price anyway. When the owner came in he explained that the cost of a shared room was only $25 for three people.

-- Jim Skipper

[egofood.livejournal.com]

It's a misplaced sign for the bellhop:
10+10+10-1-1-1-2 = 25
10+10+10-1-1-1+2 = 29