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Just A Girl
11-21-2000, 11:20 PM
Ok...my psychology teacher was kicking himself today because he couldn't figure this riddle out. While the answer can be arrived at by logic, there's not a definant answer but rather an explaination which is hard to simplify. (Well..for me anyway) Here it is:

3 men go to check into a hotel. The guy at the counter tells them that it will be \$30 for one room. The men decide to share a room, and split the cost evenly; that is, each man pays \$10. Later into the evening, the "behind-the-counter guy" discovers that the room was actually \$25, not \$30, and immediately sends a bellhop to the room with \$5. The bellhop realizes it will be difficult to split \$5 three ways so he pockets \$2, and gives each man back \$1. This means that each man has now paid \$9 in his share of the room instead of \$10. However, \$9 multiplied by 3 is \$27. Adding in the bellhop's pocketed \$2, that makes a total of \$29. So where'd the other dollar go?

While I know the basic idea of why this is so, I want to know if anyone has heard this riddle before and maybe has seen a simplified answer? Anyone else, give it a try!

dpr
11-21-2000, 11:23 PM
Oh god. Not again.....

This starts arguments around here. Just don't ask about the three doors and the odds being 50-50 or 1 in 3 please...

SPOOFE
11-21-2000, 11:26 PM
[Homer Simpson]

"It's a ring toss."

[/Homer Simpson]

(Hint: You don't multiply the numbers at the end. 30-5=25. 25+3=28. 28+2=30)

Sublight
11-21-2000, 11:26 PM
Try here:

http://www.straightdope.com/classics/a910621.html

--sublight.

Danalan
11-21-2000, 11:26 PM
Haven't you heard this one before? It is a fairly well-known example of false logic.

The key is in the two additions, which should be separate. The men indeed paid \$9 each for the room, for a total of \$27. However, one should not add the bellboy's \$2 to that amount, but subtract the \$2 from the \$27 to get \$25, the actual amount charged.

Kat
11-21-2000, 11:27 PM
Simplified:
Hotel keeps: \$25
Bellboy keeps: \$2
Man #1 keeps: \$1
Man #2 keeps: \$1
Man #3 keeps: \$1
Total: \$30

(25 + 2 + 1 + 1 + 1=30)

The way the "riddle" is worded, you count the bellboy's \$2 twice and don't count the three men's \$1 each (\$3 total) at all.

Just A Girl
11-21-2000, 11:28 PM
I didn't say anything about odds or doors! Seriously, I'm asking because I told my teacher I'd post it and see what people said. He was going nuts over this thing. I'm not trying to cause a problem...I'm just an innocent little girl! ;)

For dpr's sake guys...don't get all bent out of shape over it...I'm just curious!

Just A Girl
11-21-2000, 11:31 PM
Originally posted by Danalan
Haven't you heard this one before? It is a fairly well-known example of false logic.

The key is in the two additions, which should be separate. The men indeed paid \$9 each for the room, for a total of \$27. However, one should not add the bellboy's \$2 to that amount, but subtract the \$2 from the \$27 to get \$25, the actual amount charged.

awesome....that's what I'm looking for. See, I figured out the whole adding thing and the "false wording." But the nature of logic problems is to have a more simple explanation and that's exactly it. Thanks a ton. :D

Danalan
11-21-2000, 11:36 PM

(sigh of relief that I seem to have gotten it right, and so avoid the wrath of the collective SDMB)

Mac Guffin
11-22-2000, 01:17 AM
Back when I had to do math for a living, someone told me this riddle, and it took me almost a full day and night to figure it out. I came apon the answer in bed, at 4 am while staring at the ceiling going insane from it.

Before I arived at the correct answer covered here, I also came up with this false answer.

Later that same night, Two more guys check into the same motel, are told the room is \$30 and decide to split it by paying \$15 each. Later the "behind the counter guy" realizes that he made the mistake again, and calls the bellhop back with another \$5 in \$1 bills. the Bellhop, now overcome with greed from the earlier money, takes three dollars and gives each of the two guys a dollar each.

so each man, having paid \$14 times two, paid a total of \$28 dollars, plus the three the bellhop kept makes \$31. there's yer extra dollar you lost earlier.

I realize that the same false logic applies here, but that one almost made my brain leave my head for good.

dpr
11-22-2000, 01:45 AM
Sorry JaG, it's just that some of the logic problems posted here have started wars (or at least minor revolutions).

I was scared..... nothing personal...

Jack Batty
11-22-2000, 10:38 AM
Just A girl, you left out the most important part of the riddle.

The name of the hotel is The Gry Inn, which in itself answers at least one other question.

c_goat
11-22-2000, 10:43 AM
Originally posted by Just A Girl
Ok...my psychology teacher was kicking himself today because he couldn't figure this riddle out.

That's pretty bad. I think the SD will never eradicate ignorance as long as this "riddle" keeps circulating.

AWB
11-22-2000, 11:36 AM
Originally posted by Just A Girl
Ok...my psychology teacher was kicking himself today because he couldn't figure this riddle out. While the answer can be arrived at by logic, there's not a definant answer but rather an explaination which is hard to simplify. (Well..for me anyway) Here it is:

3 men go to check into a hotel. The guy at the counter tells them that it will be \$30 for one room. The men decide to share a room, and split the cost evenly; that is, each man pays \$10. Later into the evening, the "behind-the-counter guy" discovers that the room was actually \$25, not \$30, and immediately sends a bellhop to the room with \$5. The bellhop realizes it will be difficult to split \$5 three ways so he pockets \$2, and gives each man back \$1. This means that each man has now paid \$9 in his share of the room instead of \$10. However, \$9 multiplied by 3 is \$27. Adding in the bellhop's pocketed \$2, that makes a total of \$29. So where'd the other dollar go?

While I know the basic idea of why this is so, I want to know if anyone has heard this riddle before and maybe has seen a simplified answer? Anyone else, give it a try!

This is because he's adding together the wrong dollars.

The \$27 that the guests paid for the room consists of the \$25 that front counter has plus the \$2 that the bellhop kept. To that, he's re-adding the \$2 that the bellhop kept. This doesn't represent the total.

Or algebraically: Divide the \$30 into three parts:
Let
A = Final charge for room (\$25)
B = Amount that bellhop kept (\$2)
C = Amount refunded to men (\$3)

so A + B + C = 30

But the riddle is basically asking why:
(A + B) + B <> 30

Of course it doesn't, because it doesn't include C and it double-includes B.