"All words are symbols that represent unspeakable realities. Which is also why words are magical." (Donald Miller tweet)

Tuesday, January 12, 2010

a puzzle for you

Looking for a smart person, please.

A number of us have been puzzling over this question for the last several days. Monopoly money has been passed out, in an effort to solve it. A math teacher was even recruited, who muttered something about having seen this before, but just can't remember the exact answer.

Hmph.

I bet he doesn't know.

Do you?

Here's the scenario.

Three guys go to a hotel. (I don't know why. It doesn't matter. Maybe they were a touring band.)

The manager tells them that the hotel room is $30. So they each pitch in $10, and presto, the bill is covered.

After the guys head to their room, the manager realizes he overcharged them - the room is only $25.

So he hands $5 to the bellhop (are people called bellhops anymore? I don't know if I've ever seen anyone called a bellhop, except in the movies), and tells him to take it to the three guys.

The bellhop, however, had not been tipped. (Clearly these three guys have never seen a movie.) So he's annoyed, and keeps $2 for himself. Knocks on their door, hands them back $3, and leaves.

So each guy receives $1 back from the original $10 he put in.

Which all makes sense, right? Right.

Unless you do the math.

Because if each guy put in $10, and each guy got back $1, then each guy actually paid $9.

9 x 3 = 27.

Add 2 for what the bellhop took = 29.

Where, oh where, did the other dollar go????

I am in need of my brain for other endeavours, so if one of you could please tell me the answer to this question, that would be great. After all, that's what you're here for, right?

8 comments:

Kelly said...

i've always hated these puzzles. they make my head hurt, and by the time i finish reading them i don't care.

and i'm the kind of person that puts it right out of my brain, so it won't hurt anymore.

so i can be of precious little assistance to you.

Anonymous said...

forwarded the question to my parents because me, I am not friends with numbers!!
Kathryn

Anonymous said...

Patty this is from the internet-I shamelessly copied it because I don't have time this morning to give you the non-plagiarized version. I had seen the puzzle before so I knew it was out there.I did leave the credit at the bottom--Heidi

"This actually isn’t as much a math problem, as a logic and semantics problem. It took me a few minutes to spot the logical fallacy in this problem. I knew it was there, but it was difficult to spot nonetheless.

This is a semantic fallacy. The premise is false, which you can see when you work the equation backwards. The men do pay a total of $9.00 each (total of $27.00) for the room, but only after you add in the amount they tipped the owner. They paid $25 dollars for the room and they gave the owner $2 as a tip. ($25 + 2 = $27.00). At this point the only thing to add back in to get to the original $30.00 is the $3 the men received as a refund. ($27 + $3 = $30)

Or to simply it further:
There is a misdirect in the problem when it says that when you do the math each man paid $9 each for the room, plus $2 tip. They don't. They pay a combined price of $25.00 plus the $2 tip. The problem sets up a set of facts:

* $30.00 was originally given to the hotel owner
* Correct price of the room = $25
* Each man receives $1 dollar refund = $3
* The owner receives a $2 tip
* $25 for room + $2 tip for the owner = $27
* $30 - $27 = $3 which is how much the men receive back as a refund.


Those are the facts. Once you separate those out, you can see the misdirect in the puzzle. There isn't a dollar discrepancy as listed, all the money is accounted for.

Wording things in misleading ways is what allows swindlers to make a living. By wording it the way they have in the problem, you actually add in the $2.00 to the owner twice, and you don’t add in the $3.00 rebate to the men at all, which leaves you short $1.00.

Cynthia Kirkeby
ASK ClassBrain

Kelly said...

now see ...

my brain hurt more reading the answer than reading the question.

that's why i just look at pretty pictures! ;)

Anonymous said...

Hmmm, sounds like the harmonized GST.

Meredith said...

Here's where the problem lies in the original question:

"Because if each guy put in $10, and each guy got back $1, then each guy actually paid $9.

9 x 3 = 27.

Add 2 for what the bellhop took = 29."


That sentence is a misdirect. You don't add $2 for what the bellhop took, because the $27 is the $2 the bellhop took plus the price of the room.

The other three dollars are what they got back.

So they did spend a total of $9 each for a total of $27 ($25 for the room and $2 for the tip). The $3 left over is their change.

chRistine said...

she's right : 9x3 is the room plus tip. THAT equals 27. The other three dollars is the amount (3x1) each man got back. Semantics, not a puzzle ;)

Anonymous said...

That's easy. 3x7=30.