Wizard
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Wizard
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August 14th, 2010 at 3:16:03 PM permalink
Three guests check into a hotel room. The clerk says the bill is $30, so each guest pays $10. Later the clerk realizes the bill should only be $25. To rectify this, he gives the bellhop $5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guests didn't know the total of the revised bill, the bellhop decides to just give each guest $1 and keep $2 for himself.

Now that each of the guests has been given $1 back, each has paid $9, bringing the total paid to $27. The bellhop has $2. If the guests originally handed over $30, what happened to the remaining $1?
It's not whether you win or lose; it's whether or not you had a good bet.
Nareed
Nareed
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August 14th, 2010 at 3:25:59 PM permalink
If I say instead, "Each guest has $1 and the bellhop has $2, which totals $5," then there's no missing buck.
Donald Trump is a fucking criminal
Wizard
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Wizard
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August 14th, 2010 at 3:33:20 PM permalink
Quote: Nareed

If I say instead, "Each guest has $1 and the bellhop has $2, which totals $5," then there's no missing buck.



Yeeeeeeeeees. But much like the two envelope problem, where is the FLAW in the logic of my solution?
It's not whether you win or lose; it's whether or not you had a good bet.
mkl654321
mkl654321
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August 14th, 2010 at 4:52:33 PM permalink
Quote: Wizard

Yeeeeeeeeees. But much like the two envelope problem, where is the FLAW in the logic of my solution?



The flaw is in asking the question at all, as in it being conceivable that somehow in these simple transactions, a dollar could simply have disappeared into thin air. Thus do I cut the Gordian Knot of mathematics with the sword of logic.
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
mkl654321
mkl654321
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August 14th, 2010 at 4:56:55 PM permalink
Quote: Wizard

Yeeeeeeeeees. But much like the two envelope problem, where is the FLAW in the logic of my solution?



The flaw is in adding numbers that have nothing to do with one another, differences, remainders, whatever.

Each guest owed $8.33, overpaid by $1.66, and received back $1 of the overpayment. The remaining 66 cents each (rounding up, $2) was purloined by the bellboy. Simplissimo.
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
DorothyGale
DorothyGale
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August 14th, 2010 at 5:07:22 PM permalink
Mr. W,

Instead of pointing out the flaw ... which is a big banana ... I'll just say that this is Enron accounting ... mixing up Equity Transfers with Accounts Receivable ... just turn this accounting method into a money making machine and who knows, in a few years maybe you'll be testifying before Congress ...

It is so boring here ... so flat ... so damn flat ... is there a 3-rd dimension? I mean really, is there?

--Dorothy
"Who would have thought a good little girl like you could destroy my beautiful wickedness!"
Wizard
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Wizard
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August 14th, 2010 at 6:35:38 PM permalink
Right, the flaw is in mixing money paid and money received. The question was, "Now that each of the guests has been given $1 back, each has paid $9, bringing the total paid to $27. The bellhop has $2. If the guests originally handed over $30, what happened to the remaining $1?"

The problem is that the $27 the guests paid included the $2 the bellhop received. So that $2 is being doublecounted. Money paid should balance with money received.

Money paid = $27 ($9 from each guest)
Money received = $27 ($25 to the hotel and $2 to the bellhop)

The other $3 is money that remained with the guests.
It's not whether you win or lose; it's whether or not you had a good bet.
Doc
Doc
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August 14th, 2010 at 6:46:19 PM permalink
Very well done, Wizard. I thought this problem was so old that the question and the solution were universally known by small children. Perhaps not. Anyway, that is why I made reference to the slick ruse of the problem statement in one of my posts is the two-envelope thread. Hope whatever I said there didn't spoil anyone's entertainment here.
Nareed
Nareed
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August 14th, 2010 at 6:57:58 PM permalink
Quote: Doc

Very well done, Wizard. I thought this problem was so old that the question and the solution were universally known by small children.



Oh, you're thinking of this:

You face a choice between two doors, labeled A and B. One leads to freedom, the other leads to a dungeon. Naturally you don't know which is which. Each door has a guard. One guard always lies, the other always tells the truth. Again you don't know which is which. You are allowed only one question to either guard (one question total). What do you ask?


Here's one possible solution
Donald Trump is a fucking criminal
NicksGamingStuff
NicksGamingStuff
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August 14th, 2010 at 7:08:06 PM permalink
I say you ask either guard which door is not to freedom, the lying one will tell you which one is to freedom and the truthful guard will tell you the truth!

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