3 men go to a hotel and explain to the cashier that they would like to share one room, and need the cheapest room because they do not have much money.

The clerk provides them with a room for $30, but realized after they went to their room that the room fee is only $25, so the clerk sent the bellhop up to the room to give the men their money.

Since it was hard to give exact change, the bellhop asked if it was okay if he gave each of them $1 back and kept $2 for the tip.  The men agreed.

Each man initiall paid $10, but got $1 back so they actually paid only $9.

$9 x 3 = $27 plus the $2 for the tip equals $29.

Where did the other dollar go?
 

Jim  

Hi

Quote (Jim):

$9 x 3 = $27 plus the $2 for the tip equals $29.

Should be :

$9 x 3 = $27 minus the $2 for the tip equals $25.

And that is what they paid : $25 for the room + $2 the tip = $27.

So there is no extra dollar to chase.

Feherke.
http://free.rootshell.be/~feherke/

Let's assume the 3 men walked in with 30 one dollar bills (10 each) and that is all the money they had.  In addition, assume the hotel just opened and had no change.

The hotel clerk gave the bell hop the $5 change back in ones from the money the men initially gave him.

Therefore, there is $30 only in the hotel.  The men each have 1 dollar in their pocket (from the bellhop) and are out $9 each for the room, but $9x3 =$27 and $2 for the tip only equals $29, but the started with $30.

What explains the missing dollar?

Jim  

There is no missing dollar.
At the end of the day, each man has $1 in his pocket for a total of $3, the bellhop has $2, and the hotel has $25
25 + 2 + 3 = 30.  All square.

==> ...are out $9 each for the room, but $9x3 =$27 and $2 for the tip only equals $29
The $9x3 = $27 already includes the tip.  It's $25 for the room and $2 for the tip.  You cannot add the tip a second time to go from $27 to $29.

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>Therefore, there is $30 only in the hotel
No! There WAS $30 in the hotel, until the hotel refunded $5. Now there is $25 "in the hotel".

At the end of the transaction, the hotel earned $25 and the bellhop earned $2. Which adds up to $27, which is exactly what the 3 men spent ($27). Credits = debits. No missing dollar.

Puzzle already posted here:
thread1551-1207841: Where's the missing dollar?

Pretend the hotel is a sealed system; once the three men walk in with their 30.00, no more come or out.  Now they gave the bellhop their 30.00.  The bellhop gives the desk $25.00, leaving the bellhop with $5.00. The Bellhop gives the men back the $3.00 change, leaving $2.00 in his pocket. $25.00(Desk) + $2.00(Bellhop) + $3.00 (change) = $30.00 (Paid). Sum of the payments = sum of the debits: Books are balanced.
     What is happening here is that the way the story is told results in the tip being added to the tab twice, resulting in a bill for 29.00, instead of $27.00.  The men paid 25.00 in total for the room, and paid the hop a 2.00 tip = 27.00, or 9.00 ea

In France, we know this problem, but with a bottle of wine !!
3 mens drink a bottle in a cafe. It costs 15 €, so each man pays 5 €.
But the barman noticed that he made a mistake, the bottle costs only 10 € etc, etc.

I did not see that this puzzle was already posted.  I apologize for the repeat.

The best solution I come up with is there is no missing dollar because the math problem changed.  The math problem was originally 3 over 30 or 10 each, and then it changed due to clever wording to 3 over 27 + 2 for a tip which gave a new denominator of 29.  The difference of the first denominator of 30 and the second of 29 is the "so called" missing dollar.

Jim  

Quote:

and then it changed due to clever wording

Deliberately misleading the reader by using the wrong word for the situation is hardly what I'd call "clever".

Dan

 

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Quote (BillyRayPreachersSon):

Deliberately misleading the reader by using the wrong word for the situation is hardly what I'd call "clever".

"Deliberately misleading the reader by using the wrong word for the situation" is precisely WHY it's clever.

We'll have to disagree on that point, then.

Generally, I prefer puzzles where I have to use logic, skill, or deduction to find an answer based on fact or truthful statements. I hate it when I have to also work out what is deception and what is not... perhaps that's why saying it was 'clever' to deceive grated so much.

Dan

 

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Dan, I can understand your point. I guess it comes down to your expectations of the problem. To me, it's a variant of the old "1 = 2" fallacy proof:
http://www.innovatia.com/Design_Center/Proof_that_2=1.htm

In both situations, you are give a premise, the steps of which all seem logical. Then, you get a conclusion that is obviously false, and you realize that the premise must have a mistake somewhere... but where?

Similar to a magic trick, those puzzles involve misdirection. The "3 men / hotel room" puzzle is clever (IMO) because the misdirection works... and really WOULDN'T work with other numbers. Only because the resulting numbers are close (29 and 30, leaving a 1 dollar difference) does the sleight of hand work. Double the numbers, and it's not really impressive at all.

the premise must have a mistake somewhere... but where?
Here:

Quote:

Dividing out the common term, (x - y) results in

You can't divide by zero ...

There is math problem here and that is noting the demoninators are different.  One is 30 and one is 29 and that the difference is 1.

This problem is often used by math teachers.

Maybe my phase of clever wording through you off.  This is unlike the old joke, what is black and white and read all over with the answer being a newspaper.  The person is not able to figure it out because of clever wording and you cannot see how read is spelled.

There is a math problem here.



 

Jim  

Well, what I want to know is, did the hotel clerk give a funny look when the 3 men wanted just 1 room? And how many beds were in the room? And what scene did the bellhop find when he entered the room with those 5 dollars?

p5

It went where money always goes -
Taxes, User Fees, and an Enhanced-911 surcharge!