Another brain workout...
 

Three men on a business trip get screwed out of their hotel reservations, so they're forced to try to find rooms at a local inn.

The only inn in town with a vacancy has only a single room, so the men decide to share it.

The room costs $25 for the night. Unfortunately none of the men have bills smaller than $10's, and the innkeeper doesn't have any change. So each of the men pays $10, and the innkeeper tells them, he'll send the bell-hop up to the room with change as soon as he's got it.

An hour later the bell-hop arrives at the room with five $1 bills. To avoid having to split up the five bucks among three people, the men each take a dollar, and let the bell-hop keep the remaining two bucks as a tip.

So, if each of the men has now spent $9, plus the $2 tip, that's only $29... where's the missing dollar from the original $30?

3 x 9 = 27 that they spent ... 25 for the room + 2 for the tip

<elzar>BAMM!</elzar>

Yeah, but they started out with $30 total.

They all spent 9 1/3 dollars. The bellhop was given 3*2/3 dollars as a tip.

Edit: close but not quite. I'll nail it down in next post (after the next one I already did. Dean can solve that paradox.)

Or maybe it was inflation? :p

The room cost each man 8-1/3 dollars. They each paid $10, got $1 change, and tipped 2/3 of a dollar to the bellboy.

And the hotel has $25, the bell hop has $2, and each guest has $1 (x3) = $30 that they all started with.

Or, they collectively paid $25 (for the room) and $2 (for the tip) for a total of $27. $27/3 = $9.

The total of $29 is gotten from adding the tip twice and not factoring in the $5 change. Also, known as incorrectly adding everything together.

Next up... what is the average velocity of an unladen swallow?

or were they staying at the ponderosa and perhaps slid that dollar down a g string for a shake-shake at the orchid??

I'm not saying there actually is a missing dollar. I'm trying to find the logic error in the original story. So far I got nothing.

Look at it this way.

Each guy takes out a $10 bill. That's a total of $30. No logic error there.

Now each guy puts away a $1 bill. They've each spent $9. No logic error there.

The bell-hop has his $2 tip. No logic error there.

$9 x 3 + $2 = $29. No logic error there.

However, we agreed that the original total was $30. Where's the error?

You subtract the $2, not add it yo.

Michigan > Cal. Poly

There is the error.

They paid $9 after the change.

$9 x 3 = $27 (after tip)

but, there was $2 dollar tip, so you need to subtract it, not add it to get the total they paid after the change and before the tip.

$9 x 3 - $2 = $25 (after change and before tip).

$9 x 3 - $2 + $5 change = $30 (before change and before tip. or, how much they paid the guy at the desk)

When they paid for the room, they spent $8 2/3. The receipt of $1 from the bellhop fosters an incorrect assumptiont hat they 'spent' $9. The missing $1/3 from each man accounts for the 'missing' dollar.

If you're looking for what in the wording of the problem causes the error, not the actual logic error itself.

Nope.

They paid $9. If they had $10, and now have $1, how did they spend $8 2/3? They don't have change lying around.

The hotel cost $8 1/3 per man. There was no change laying around, hence the bellboy bringing the singles to the room and collecting $2/3 from each in the form of 2 singles.

Edit: $8 1/3. not 2/3.

They each spent $9 dollars out of pocket. That means they give $27 to the hotel. The hotel gives the bellboy $2 for his tip, which leaves them with $25 for the room.

Yes, the hotel cost $8 1/3 (despite the fact that is impossible :p), but they paid $9 total.

Like Nick and JC are saying. The logic error made in the original story is that you can attempt to add up the final out of pocket cost, plus the tip, and expect to get the same number as the pre-change cost.

The tip has to be subtracted from the $9 x 3, which gives you the $25 room cost.

Yes. The $9 breaks down as $8 1/3 to hotel and $2/3 to busboy for each man. I was eplaining to scott why the wording of the problem makes you come up with $29.

Not impossible at all. You paid $2.XX9 a gallon for gas at your last fillup didn't you?

Nope. I $35.09 for my last fillup. At $2.699 / gallon x 13 gallons, that technically totals $35.087, but since banks don't deal in micropayments yet, I paid $35.09.

Furthermore, if/when micropayments are done, you still won't be able to pay $1/3 because it is an infinitely repeating decimal, where as 9/10 ¢ is a distinct amount.

Ya I understood what you were saying when I read it again. You are right, just an odd way of putting it.

Yeah, I had to re-read his stuff a few times too. Its kinda convoluted, but correct.

Actually, Mike got it right. The mistake is in the phrasing of the question, in saying they spent nine a piece and added a $2 tip. They spent $9 a piece, period. 9x3=27. Then they kept $1 each, equalling $3. If they were to give up their $3 in change it would equal the original 30. The $2 tip is part of the $27 spent: 27-2=25.

Ah, the joys of working retail. . . :|


edit: already been worked out. hah. that'll teach me not to read the whole thread.

More!