Here is an unsolvable math puzzle - can you find the answer?

Question

Supposedly this riddle is world-wide known as "unsolveable". The object is to find out why the hotel owners profit is one dollar short. HERE WE GO.........There was a hotel owner who charged his 3 of his guests $10 each for each to stay at the hotel for one night. From that he earned $30 dollars. He gave the bellboy $5 out of the $30 he collected from the guests and told the bellboy to keep $2 dollars for himself and to give each guest back $1 dollar. So now the 3 guests are being charged $9 each. So you take the $9 x 3 guests that equals $27 dollars plus the bellboys $2 ......... that equals $29. Where did the other dollar go???

Answer 1

THis is an old, old problem. The guests payed a total of 27 dollars, two of which went to the bellboy and 25 to the hotel. You should SUBTRACT the 2 dollars, not add them.

Answer 2

It is well-known, but hardly unsolvable.

The $27 that the guests paid is in two parts: the $25 that they actually paid to the hotel ($30 - $5=$25) and the $2 that the bellboy kept.

By adding 27 plus 2, you're re-adding the bellboy's $2 and getting an erroneous total.

The real tally of the money is:
$25 - money kept by the owner for the room rental
$2 - tip kept by the bellboy
$3 - money given back to the guests
Total is $30. No missing money.

Let's put the same riddle together with different amounts that'll make it more obvious:
A hotel manager rents a room to 3 gentlemen for $100. Afterwards, he gave the bellboy $30 and told him to give $28 back to the guests and keep $2 for himself. So, the guests have paid $72, plus the $2 for the bellboy is $74 dollars. Where did the $26 go?

Answer 3

This is stupid.
The owner has $30 to start out with.
He gives the bell boy $5. Now the owner has $25.
The bell boy is to give $3 back to the guests and keep $2 for himself.

2+3 = 5

this $5+ $25(owner already has) = $30

At the end of the day, the owner has $25, the bell boy has $2 and the guests have a total of $3 left out of the pool of $30 and

25+2+3 = 30.

The trickery comes in when you say that each guest paid
$9x3 = $27 and the bell boy has $2 for a total of $29 . This is incorrect because the $9x3 = $27 that the three guest paid out actually INCLUDES THE $2 TIP THAT THE BELL BOY RECEIVED. The other $3 out of the $30 is in the hands of the hotel guests. Your statements leads people(or maybe just you) to believe that the $27 does not include the tip for the bell boy, and thats why this "riddle", which is actually just a story that uses a deceiving statement to try to confuse people, is stupid :-)

Answer 4

This puzzle simply asks a meaningless question, and attempts to confuse the reader by performing calculations that do not mean anything. Here's how it goes:

Hotel owner charges $10 each to three guests. Three guests each give $10 (which is all they have, let's assume) to hotel owner.

Current monetary totals:
Guest A - 0
Guest B - 0
Guest C - 0
Owner - 30
Bellhop - 0

The owner then gives $5 and some instructions to the bellhop.

Current monetary totals:
Guest A - 0
Guest B - 0
Guest C - 0
Owner - 25
Bellhop - 5

The bellhop keeps 2 dollars, and gives 1 dollar to each guest.

Current monetary totals:
Guest A - 1
Guest B - 1
Guest C - 1
Owner - 25
Bellhop - 2

That is how the totals stand at the end of the problem. You can plainly see they add up to $30. So ask yourself the following question: "Why does the problem then proceed to add the net LOSSES of the guests ($27 total) to the net GAIN of the bellhop ($2)?" The quantities are TOTALLY unrelated. Adding them together produces $29, sure enough, but the 29 is meaningless. The calculation is done simply to confuse and mislead the reader.

Answer 5

The book keeping is from teh guests' point of view. Look at it from the manager's.

He received +$30

He gave the bellboy -$5

Net so far +$25

Total: $30.


Now the bellboy takes $2and gives the guests $3. So each guest thinks he paid $9 for the room, but each really paid $25/3 = $8.33 for the room and (unbeknowst to them) tipped the bellboy $2/3 = $0.67 each.

It is the mixing of prespectives that makes it appear that a dollar has mysteriously disappeared. The manager has all $30 accounted for.

Answer 6

Wait...he charges $10 to begin with but then gives 3 back...
so that's 10x3=30-3=27-2(the bellboy)=$25 which is what he is left with...
wait... (basically u say that he charges them $9 as he gives $3 back to the 3 guests)so...
$9x3=$27-2=$25
27+3=30
is that how you solve it?
You are not meant to plus the 2dollars from the bellboy but you are meant to plus the $3 dollars that was given to the guests because the 2dollars was already included (27) as 25 was what he was left with.
Good riddle!

Answer 7

well this is.. old haha

the hotel owners had already gotten the money, so he wasn't charging the guests any different...
it was still 10 a night, they each happened to get a dollar back.

so.. he gave 5 out of 30 to the bellboy.. bb kept 2 gave 1 dollar back to each guest.

so if you keep the equation going forward.. to say, you will see where the money was

.... lets see

yeah.. explanation is hard.


but a big WOO HOO to the people who did explain it.. haha

good job

Answer 8

Not only is it not unsolvable, it has been asked (and correctly answered) many times on Yahoo answers.

The owner has 25 and the bell boy has 2, where is the problem?