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.