Where's the missing dollar? 1

[kaht]

I was hesitant to ask this question earlier because it didn't really have a whole lot to do with programming. But after the question about the lottery turned into more of a math discussion I figured this would be fair game.

Before I ask the question let me add that it doesn't really have an answer because the logic in the question is flawed. When I was in high school I did get my physics teacher to blow a whole class period trying to figure it out though, so it's always stuck in my head


[The question]
3 businessmen are on a trip and share a hotel room for the evening. The bill comes to 30 dollars (it's a cheap hotel) so each businessman pays his even share - 10 dollars. They head up to their room and the cashier realizes he's made a mistake. He forgot that there's a special rate for the evening and that he should have only charged the businessmen 25 dollars (it's a REALLY cheap hotel). The cashier then instructs the bellboy to run up to the room and refund the 5 dollars to the businessmen. With his incredible insight, the bellboy realizes that the businessmen cannot easily split the 5 dollars between the 3 of them. So instead he pockets 2 dollars and returns 3 dollars to the businessmen. The 3 dollars is returned and each businessman gets a dollar back.

At this point each businessman has payed 9 dollars out of his own pocket, making a grand total of 27 dollars paid for the room. Combine that with the 2 dollars that the bellboy kept yields 29 dollars. So, where's the missing dollar?

-kaht

[small] <P> <B> <P> <B> <P> <B> <P> <B> <P> <B> <P> <B> <P> <B> <P> <B> <P> <B> <P> <B> <P> <B> <P> <B> <P> <B> <P> <.</B>[/small]
[small](He's back)[/small]

 

[Stella740pl]

I guess that the saddest twist to this story in the 21st century is that the story-teller has to preface the story-riddle, explaining that "3 men in 1 motel room" has nothing to do with a perverted lifestyle.

Just start it like this:
"Three very cheap businessmen are on a trip and, in order to save some money, share a very cheap hotel room for the evening." ;-)

 

[franklin97355]

Or multiply all values by 10.

The answer is "42"

 

[GwydionM]

Make it 300 dollars charged. It should be 250. The cashier takes back 50 dollars for a refund, but decided to keep 20 and give each of them ten.

Each businessman has paid 100 dollars and got 10 back, net payment of 90, times three equals 270.

The hotel got 250. The cashier stole 20, that accounts for the 270.

Or if he'd refunded 48 dollars, 16 each, they would each have paid 84 dollars, total 252. Adding this to the 2 dollars that this alternative cashier stole gives you 254, way out. Adding the 250 dollars received by the hotel to the 2 stolen is also 252, no missing dollars.

------------------------------
An old man who lives in the UK

 

[Gooser]

Is the $30 an hourly rate?

--just wondering--

Gooser

 

[Stella740pl]

I thought, Pgould1 had a problem not with the prices being low, but with the fact that "in the 21st century ... the story-teller has to preface the story-riddle, explaining that "3 men in 1 motel room" has nothing to do with a perverted lifestyle"?

 

[kaht]

Stella, I believe the humor lies in the fact that hotels with low prices are notorious for being used for only perverted purposes.

-kaht

Looking for a puppy?

[small]Silky Terriers are small, relatively odorless dogs that shed no fur and make great indoor pets.[/small]

 

[ESquared]

I thinkt he only reason there's any disagreement about the Monty Hall problem is because of poor logicians, not because of poor logic. It's quite simple, really.

 

[strongm]

Oh oh ...

 

[ESquared]

laugh

Just use the "extremes" technique. By pushing the number to an extreme it simplifies the problem.

There are a million boxes, one of which randomly contains a prize. You are allowed to choose one and do so. The contents of the remaining boxes you did not choose then get combined into one big box.

Now, you can keep your original box (1 in a million chance) or you can switch to the big box (999,999 in a million chance). What do you do?

A little thought shows that "combining n boxes into one big box" is the same as "removing n-1 boxes known to be empty."

There's a gigantic wikipedia page on this which could really use a simpler explanation like the above.

 

[strongm]

Here we go ...

 

[franklin97355]

What does that have to do with the original puzzle? I'll take the big box.

The answer is "42"

 

[ESquared]

Sorry about the off-topic wandering. And I meant no disrespect for anyone! In fact, I'd be content if we all just forgot the off-topic parts of this thread... silly me.

 

[franklin97355]

No disrespect, just curious.

The answer is "42"

 

[BobRodes]

That's all right, esquared...after all, strongm started it. ;-)

As for the original topic: although I am NOT an accountant, nor do I pretend to any skill in the subject, it strikes me that it's the sort of thing that accountants deal with all the time. I would say that the puzzle is attempting to introduce confusion between assets and liabilities, debits and credits. The way to introduce the confusion is to suggest that the boy's $2 credit goes also to the hotel as a $2 credit, which is of course wrong. The fact that the boy is a representative of the hotel is a compelling reason to perceive them as one entity. It's also irrelevant...a master touch! So, in fact, the boy's $2 credit is of course a $2 debit to the hotel.

So, the transactions appear to be:
1. credit hotel 30, debit businessmen 30.
2. debit hotel 5, credit bellboy 5.
3. debit bellboy 3, credit businessmen 3.

Total assets to hotel, 25. Total assets to bellboy, 2. Totall assets overall, 27. Total liabilities to businessmen, 27.

All in balance, all in harmony....thanks to Amatino Manucci.

Bob

 

[traingamer]

This riddle is older than me. (And that's saying a lot.)

Greg
"Personally, I am always ready to learn, although I do not always like being taught." - Winston Churchill