Where's the other dollar? An error in math?
This is a mathematical story that makes it seem as if there's a glitch in math. There are 3 people who go into a hotel to stay the night. A hotel room costs 30 dollars, so each person pays 10 dollars so all 3 can share one room. After the people find their room, the hotel manager realizes that he's made a mistake. Rooms are actually 25 dollars instead of thirty. So the hotel manager calls in his bell waiter, and asks the bell waiter to take 5 dollars back up to the room, and split the 5 dollars evenly amongst the 3 people. As the bell waiter heads up to the room, he realizes that $5.00 can not be split evenly amongst 3 people, so instead he decides to give each man one dollar back, and keep 2 for himself. Now, all three people had ORIGINALLY payed $10.00, but because they each received one dollar back, each person only payed $9.00, plus the bell waiter had $2.00 in his pocket. 9 times 3 = 27, + the 2 in the bell waiter's pocket equals 29. Where's the remaining dollar?
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Winnopeg on Jun 02, 2007
Trippy.
dyar on Jun 02, 2007
There is no missing dollar. The men paid 27 (3x9), the hotel has 25 and the waiter has 2 = 27, all monies accounted for.
but if you really want to know where it is:
The following day two men go and stay at the same hotel and pay $30 and go off to their room. the manager forgot again that it was only $25 and gave the bellboy $5 to give to them. The bellboy this time keeps $3 for himself and gives $2 back to the men. Take that away from the $30 they originally paid makes $28 plus the bellboy's $3 equalling $31!
There's your missing dollar!
Steax on Jun 03, 2007
The trick has to do with the fact that we're assuming the total amount of money must be 30 dollars.
The three men are paying a total of 27 dollars, which is the required 25 plus the two taken by the waiter. Each man has given 9 dollars. Yes, like dyar said.
Still a good example of a well-designed diversion.
SpacesEnd on Jun 03, 2007
dyar: I must be having a moment of stupidity, but I have no idea what you just said. For the sake of my still-in-progress train of thought, could you explain what you said a little clearer, I don't get how you're math adds up.
SpacesEnd on Jun 03, 2007
Steax: Please correct me if I'm wrong, but how is the total money NOT $30.00?
AppleGeek on Jun 03, 2007
What are you talking about, there's no missing dollar, I have it.
SpacesEnd on Jun 03, 2007
Never mind Dyar, I get what you're saying...but weren't there 30 bucks from the beginning?
dyar on Jun 03, 2007
The question is actually a trick question since it suggests that you should be adding when you should be subtracting. Another way to look it is that the Hotel has 25, the bellman 2, and each of the guests has 1 each: 25+2+1+1+1=30
SpacesEnd on Jun 03, 2007
Obviously if you were to try this in a real-life situation, the dollar wouldn't disappear. But according to the math [ 9X3+2=29 ] there's only 29 dollars. This is why I wonder if it is a "glitch in math."
SpacesEnd on Jun 03, 2007
I'm not sure what you mean by you're supposed to be subtracting.
SpacesEnd on Jun 03, 2007
Also, the first time that I was told this mathematical story-like thing, The guy telling it claimed that it's one of the two mathematical "impossibilities." (I don't know the other one.)
Liquix
on Jun 03, 2007
30 = 10 * 3
27 = 9 * 3 + 2
Well, set the + as - instead and you get what they actually payed
Liquix
on Jun 03, 2007
I can say why:
The 2 dollars to the bell waiter is included in what the guys paid. They payed 9 dollars each. 2 of those 27 dollars went to the bell waiter. So thats 25 + 2. Then add the 3 dollars they originally had to pay too. 25 + 2 + 3
ZsaZsa on Jun 03, 2007
Liquix is STEALIN UR DOLLAR! ARRGHH!
Granf on Jun 03, 2007
Liquix: I hate to break it 2 u, but 9 times 3 is 27, not 25. 9 times 3 +2 is 29, not 27. You're math is off because of this mistake.
Granf on Jun 03, 2007
You said that 27=9 X 3 + 2, this is incorrect.
Liquix
on Jun 03, 2007
Oops, sorry. Well, the last I said is correct though:
The 2 dollars to the bell waiter is included in what the guys paid. They payed 9 dollars each. 2 of those 27 dollars went to the bell waiter. So thats 25 + 2. Then add the 3 dollars they originally had to pay too. 25 + 2 + 3
Steax on Jun 03, 2007
@SpacesEnd: The original 30 dollars is only the amount that everything added up to at first, not the end amount. Eventually, each man had paid 9 dollars, and an extra 2 dollars at the waitress. There is no problem in the math - it is simply the similarity of the number 30 and 29.
The correct evaluation formula would be:
HotelMoney = (MoneyPaidPerPerson * NumPersons) - StolenMoney. This means 25 = (9 * 3) - 2.
Exactly what dyar and Liquix said.
Remember, the figure 30 only existed in reality until the point when the money was broken up again. At that point, the figure has dissolved.
Liquix
on Jun 03, 2007
This hotel story tricks us to think that the 2$ the bell waiter gets isnt counted in inside the 9 * 3.
This is the maths:
27 = 25 + 2$ the bell waiter got
Steax on Jun 03, 2007
In, fact that is not a valid formula.
TotalMoney = (MoneyPaidPerPerson * NumPersons) + WaiterMoney
is the formula used so far. The thing is, the first part is expense, while the second part is stock. Look at this:
InitialTotalMoney = (MoneyPerPerson * NumPersons) + HotelMoney + WaiterMoney
To make it easy, lets assume the Hotel and Waiter has no money (although they would need some for the $5), and assume each man only has $30.
InitialTotalMoney = ($10 * 3) + 0 + 0 = $30
Now for the second formula...
TotalMoney = (MoneyPerPerson * NumPersons) + HotelMoney + WaiterMoney
(Exactly the same formula) Now we fill it in...
TotalMoney = ($1 * 3) + $25 + $2 = $30
InitialTotalMoney = TotalMoney.
SpacesEnd on Jun 03, 2007
You're right, The way that most people (or at least me) add it up is wrong...but it's a good trick...
dyar on Jun 03, 2007
This puzzle has been around 20-30 years and still stumps people. Just Google it for more info.