Random Logic check

crazy4life • 28 October 2011 at 5:03 AM

See if you can figure out how this makes sense...

Three friends go to a motel and rent a single room for one night. The charge was $30.
They head up to their room to unpack and watch TV.
The clerk suddenly figures out he over charged them $5. He gives the $5 to the bell boy and asks him to deliver the change.
Half way up the steps the bell boy concludes that he can't split $5 evenly by 3. He pockets $2 and gives each of the friends $1.

Here is the mathematical break down of the situation:

Friend 1 Friend 2 Friend 3 Bell Boy
-10.........-10...........-10
+1.........+1............+1.........+2
=9.........=9............=9.........=2

Total it up and you get $29.
Where did the extra dollar go?

This problem was raised in my philosophy class. We came up with several ideas, but I want to get your take on it first.

so......

dionaea • 28 October 2011 at 5:29 AM

What extra dollar?

This is something really odd they're doing here, it's a return, so it's subtracted from the original 30 dollar, but you're actually adding up the return, including the dollars the bellboy DIDN'T return, that's where it goes wrong

Normally it would be:


Friend 1 Friend 2 Friend 3
-10.........-10...........-10
+1.66.....+1.66.......+1.66
=8.33.....=8.33.......=8.33

Which gives a total of 25, the amount they should have paid. But now the bellboy hasn't returned the money and for some reason your teacher has added that to the total. The total they've paid now is 27, you get 25 when you subtract the 2 from the Bellboy.

The bellboy should be -2 for the friends, since they lose 2 to him and then you get the total they should have paid.

So where did the dollar go? I'll give you a very 'Matrix' answer: There is no dollar. Only a faulty calculation. What your teacher does is make a map of gains and losses, but it doesn't show until you add the entire story. Also you can only do this with one party in mind, he's put the gains of 2 opposing parties in there.

This is the correct one, it adds up to 0
Friend 1 Friend 2 Friend 3 Clerk bellboy
-10.........-10...........-10......-30......0
+1.........+1...........+1........+5.......-2
=9.........=9...........=9........=-25....=-2

ayuzawa • 28 October 2011 at 5:36 AM

@dionaea

@crazylife4

---

my head spins...

crazy4life • 28 October 2011 at 5:39 AM

@dionaea: Thats the answer I came up with to... However trying to explain that to the group of math nerds in my philo class was very unsuccessful. They decided that it was a case of misuse of the order of operations.

They just wouldn't believe me... Oh well.

And it wasn't the teacher that gave this problem. One of the students was given it in his calculus class and he decided to share it while we were talking about metaphysics. Our poor professor had a head ache at the end of class

dionaea • 28 October 2011 at 5:43 AM

@ayuzawa

Its a nasty bugger this one, because the flaw is so hard to see. My maths and economics teacher would have seen straight away though DX

Anyhow, I think it might be better to split up the final calcutlation, that makes it more clear:

Friends:

ayuzawa • 28 October 2011 at 5:44 AM

@dionaea

lol... 😃 I don't even have an economics teacher... cos i'm not in high school? O_o

crazy4life • 28 October 2011 at 5:45 AM

@dionaea

I think how he presented it in class and asked everyone to come up with the sum of $30 is what threw everyone off. They couldn't see beyond that.

dionaea • 28 October 2011 at 5:46 AM

I did one year of compulsory economics, one year voluntary and I did a year of a subject named Management & Organization (which is a different word for just plain economics XD)

crazy4life • 28 October 2011 at 5:46 AM

@ayuzawa

College level philosophy

ayuzawa • 28 October 2011 at 5:48 AM

@dionaea

@crazy4life

oh. no wonder... *headdesks*

still gonna try to figure it out 😋

crazy4life • 28 October 2011 at 5:48 AM

@dionaea

I hate economics... I wanted to burn my book so many times!!!! And I still have to take more credits for my degree!!!!!

Accounting and finance makes a lot more since.

dionaea • 28 October 2011 at 5:49 AM

@crazy4life

Sorry, didn't see your second post there DX Anyway, you were right and these Math nerds are obviously more calculus nerds, because you're supposed to pay attention to what it is you're actually putting together XD

Edit: Actually this is a bit like accounting, so you probably had an edge on the rest, it's basically about profits/money changing hands 😊

crazy4life • 28 October 2011 at 5:51 AM

@ayuzawa

How dionaea broke it down is pretty good. In the problem you are actually trying to find how much the room cost- which would be $25. (30-5) or if you went to figure out how much the friends spent it would be $9 each. (9*3=27) and if you subtract the $2 for the bell boy you get the $25

@dionaea

The poor psychology students who are required to take the class were banging their heads on their desks the whole time. I pretty sure they thought the rest of us were just nuts.

ayuzawa • 28 October 2011 at 6:17 AM

@crazy4life

wait...isn't that cos you added for the bellboy... when you should have subtracted?

crazy4life • 28 October 2011 at 6:24 AM

@ayuzawa
yup. The bell boys "tip" needs to be subracted

ayuzawa • 28 October 2011 at 6:28 AM

@crazy4life

your teacher is misleading =_=

crazy4life • 28 October 2011 at 6:33 AM

@ayuzawa

It wasn't my teacher who gave us the problem... She was banging her head against the wall with all the psychology people.
It was a math major- his WHOLE calculus class couldn't understand it.

Personally I find that funny.

ayuzawa • 28 October 2011 at 6:37 AM

@crazy4life

oh. no offence, but the calculus class you're referring to is narrow-minded. like REALLY narrow-minded.

crazy4life • 28 October 2011 at 6:48 AM

@ayuzawa

lol. What more do you expect from a group of people who are going to spend their lives looking at numbers? I know one girl who has taken calculus 3 (the highest cal class at our school) who couldn't find an answer to this. Most of them HATE word problems anyways.

It always makes me shiver when I think of all the math classes ABOVE Calculus 3. What practical purpose could their be for it when most of us wont even us Algebra?

ayuzawa • 29 October 2011 at 8:01 AM

@crazy4life

lol... but seriously.... if they ignored the fact that it adds up to $29 dollars, and got the correct sum, they would have figured it out cinchily =_=

lily- • 29 October 2011 at 8:19 AM

@crazy4life
Good sum, it makes people think. I've started calculus in my C1 class, though I still got it. I don't think people think out of the box for things like this when they should, that's why they get it wrong.😋

Deleted • 29 October 2011 at 8:54 AM

Ok, so iv heard this one before😊 First off, you must think like this. The charge was $30(that was split, so $10 paid by each)they overpaid by five, which is $35. They got $1 back each, the bellboy kept $2 which = the five dollars overpaid. There AREN'T any dollars missing😊

Or did I mess up, and they only had to pay $25 dollars? if that's the case, still no dollars are missing😊 They each got $1 back, the bell boy kept two= $30 Three guests got paid one of the five dollars each. Totaling three dollars, bellboy kept two which equals five;) They WANT you to THINK some of the money is missing, but NONE of the money is ACTUALLY missing😸

EDIT:
WH00T!!!! The first time my logic isn't insane sounding xD