OT: math question

[trumpetr]

This might have been better put into the monthly joke thread, however,it's a math question-- so, have fun, and post your theories:


Three friends check into a hotel for the night and the clerk tells
>them the bill is $30, payable in advance. So, they each pay the
>clerk $10 and go to their room. A few minutes later, the clerk
>realizes he has made an error and overcharged the three by $5. He
>asks the bellhop to return $5 to the three friends who had just
>checked in. The bellhop sees this as an opportunity to make $2 as he
>reasons that the three friends would have a tough time dividing $5
>evenly among them; so he decides to tell them that the clerk made a
>mistake of only $3, giving a dollar back to each of the friends. He
>pockets the leftover $2 and goes home for the day! Now, each of the
>three friends gets a dollar back, thus they each paid $9 for the
>room which is a total of $27 for the night. We know the bellhop
>pocketed $2 and adding that to the $27, you get $29, not $30 which
>was originally spent. Where did the other dollar go????
>

[sKilled]

There is no money missing -
The taxman stole it.

[trumpetr]

There is no money missing -
The taxman stole it.

That was my first thought- keep on thinking

[sKilled]

No, honestly, the flaw is in the calculation. One assumes that having paid $10 dollars each, and getting $1 dollar back each, that makes $9 actually paid each (true). And that times 3 equals $27 (true). This is the amount actually paid by the three men, as $30 minus the $3 which they got back equals $27. Minus the $25 dollars which it actually cost them equals $2, which was nicked by the bastard bellhop.

[sKilled]

In numbers

$30 (original bill)
-$ 5 (refund)
=$25 (actual bill)

$ 5 (refund)
- $ 2 (nicked by the bellhop)
=$ 3 (returned to the poor bastards)

Therefore
$30 (what they originally paid)
-$ 3 (what was returned to them)
=$27 (what they have now paid)

$27 (what they paid)
-$25 (what they were supposed to pay)
=$2 (thieved by the bellhop)

I didn't take mathematics 102 at the University of Auckland for nothing (no it cost me about $540).

[632 Regal]

dead on, if you reverse think it then it dont add up.

[sKilled]

Thanks Jeff, btw, dig the sig. The crap we humans get up to without so much as an afterthought to the consequences - see DDT, agent Orange, smoking etc etc.

[trumpetr]

No, honestly, the flaw is in the calculation. One assumes that having paid $10 dollars each, and getting $1 dollar back each, that makes $9 actually paid each (true). And that times 3 equals $27 (true). This is the amount actually paid by the three men, as $30 minus the $3 which they got back equals $27. Minus the $25 dollars which it actually cost them equals $2, which was nicked by the bastard bellhop.

After reading thru that again,,you are right. It is the bastard bellhop!!

[sKilled]

Thanks Trumptr, and congrats on hitting 100 posts!

[nuclearfusion]

The actual room cost is $25, not the $30 originally paid by the hotel guests. Thus the seemingly great conundrum (?) appears only because the problem is arranged in a disengenous manner.

You are NOT trying to make $27 + $2 = $30 which the problem suggests you should be doing and of course does not work... (hence the apparent mystery)

You should rather be trying to make $27 - $2 = $25, which of course it does.


In both cases.


QED.


Fusion


p.s. - The implication that "30-3-2=25" should somehow be at odds with "27+2=29" is ridiculous. They are both simple arithmetic facts. More ridiculous is the implication that drives the whole thing - namely that these statements should be equal. The fact is that they are both true, but both being true does not logically require them to be equal. I'm not sure how anyone can be surprised by the fact that 30 is not equal to 29.

[trumpetr]

Thanks Trumptr, and congrats on hitting 100 posts!
Thanks, mate. This is a great forum, and I am learning heaps!. Fun to post the occasional off topic horseshitte thread, too.

[sKilled]

Hehe, how do you think I made 200+? I don't know jack about the E34 (well nowhere as much as most). But your're right, this forum rocks. Not only the copiuos amount of knowledge impressed me, but the manner which is expressed by the members - it is a very mature forum where all are treated as equals. If all forums could be like this...

[trumpetr]

The actual room cost is $25, not the $30 originally paid by the hotel guests. Thus the seemingly great conundrum (?) appears only because the problem is arranged in a disengenous manner.

You are NOT trying to make $27 + $2 = $30 which the problem suggests you should be doing and of course does not work... (hence the apparent mystery)

You should rather be trying to make $27 - $2 = $25, which of course it does.


In both cases.


QED.


Fusion


p.s. - The implication that "30-3-2=25" should somehow be at odds with "27+2=29" is ridiculous. They are both simple arithmetic facts. More ridiculous is the implication that drives the whole thing - namely that these statements should be equal. The fact is that they are both true, but both being true does not logically require them to be equal. I'm not sure how anyone can be surprised by the fact that 30 is not equal to 29.

Well spoken theory!
The actual room cost to the occupants is still $30, paid. The bellhop realized they were overcharged by $5, and went to make amends.
You are assuming that, the 'bellhop' is in the coloquial, 'cahoots', with the management/ownership, in that, the original price of the room was $25, and that the occupants were overcharged $5 and paid $30.
Breaking this down to its elements,
The original math problem remains--

[joshua43214]

its called order of operations. you have to do math in the correct order.

This is a common mind problem that good math teachers use to help students understand the need to do math in the order it is presented

3x10=30

2+(1x3)+(3x10-5)=30

[trumpetr]

its called order of operations. you have to do math in the correct order.

This is a common mind problem that good math teachers use to help students understand the need to do math in the order it is presented

3x10=30

2+(1x3)+(3x10-5)=30
You are right. I read thru it again, and I see your point, and its pretty clear that i wasnt thinking about the problem in the right order.
I see it now.

[azale]

It's best to just follow the cash flow. Each guest started with $10, now each has $1. The Hotel has $25 (for the room), and the Bellhop has $2.

I remember when I was in grade school my bus driver told me this 'riddle' and followed it up with "you can't figure it out, it's a mathematical error." I was probably in 4th grade and figured it out that night, then I tried to explain it to her the next day to no avail.

I'm just glad my bus driver wasn't a teacher.

[Morgenster]

Riddle:

You're in a hallway looking for a treasure. There's two doors. One leads straight to the treasure, the other to a painful death. You can easely access any one, but once you've made your choice there's no way back.
At each door there's a guard. Both guards know where the treasure lies.
You can only ask one question to one of the guards before making your choice.
Only problem is one of them always lies and the other always tells the truth and you don't know which one.

So you only get one question and answer. What question do you ask to know for sure which door to choose?

[joshua43214]

Ask either gaurd to ask the other gaurd where the treasure is and to tell you the answer.

[Morgenster]

Ask either gaurd to ask the other gaurd where the treasure is and to tell you the answer.

I can see it working out, but given that both guards know which one is lying and which one is not, you can simplify that.
Still a very creative correct answer that I hadn't discovered yet.

[Jon K]

The problem just tries to trick you buy identifying that they paid $27 total... but , as already pointed out, the fair was $25 not $27.

[nuclearfusion]

Well spoken theory!
The actual room cost to the occupants is still $30, paid. The bellhop realized they were overcharged by $5, and went to make amends.
You are assuming that, the 'bellhop' is in the coloquial, 'cahoots', with the management/ownership, in that, the original price of the room was $25, and that the occupants were overcharged $5 and paid $30.
Breaking this down to its elements,
The original math problem remains--

No, it doesn't.

The original post deceptively suggests that there is some discrepancy between 27+2=29 and 30-3-2=25 which there is not.

The real problem is in the suggestion that 27+2 somehow describes the situation; which of course it does not. It's not $27 + $2 to the bellhop, but rather $27 - $2 to the bellhop, which gives $25 to the hotel in both cases.

QED as before.

Enjoy!

Fusion

[Mitch90535im]

Speaking of math, did you know you can go to google, key a math equation into the search field and it will return the answer.

Or, that you can go to google, key any shipper's tracking number into the
search field, and it will take you straight to the tracking page.

Or, key any airline flight number into the search fiend, and it will give you the status of the flight.

Intersting stuff I didn't know about google.

[Espen]

Speaking of math, did you know you can go to google, key a math equation into the search field and it will return the answer.

Or, that you can go to google, key any shipper's tracking number into the
search field, and it will take you straight to the tracking page.

Or, key any airline flight number into the search fiend, and it will give you the status of the flight.

Intersting stuff I didn't know about google.
I did know about the math thing.. But the tracker and flight doesnt work out for me.. (norwegian flight codes)

[gale]

I think I've seen this logic before . . .

http://faculty.fhu.edu/ldrive/Walker,Allen/Ma%20&%20Pa%20Kettle%20Math.wmv

(4 Mb)