Riddle
 

Three travelers stop at a motel and ask for a room. Manager says the room is $30 and they each pull out a $10 bill. Later, the manager comes to them with five $1 bills, and reporting he erred by charging them the weekday rate on a weekend when rooms are actually just $25. The travelers notice the five $1 bills cannot be evenly distributed among them, so they take each take $1, and the remaining $2 becomes a tip for the manager. At this moment, each traveler has paid a net amount of $9.

Three times nine is 27. Add the manager's tip and you have $29. Where did the remaining dollar go?

Because the FED has printed so much money, in the time it took to conduct the transaction the $ got devalued/lost that $1 in value.

shouldn't it be 25 for the room 2 for the tip and 1 each for the guests?

Ding ding ding. Flatbutt for the win. ;)

Flawed method of calculation Where did the actual $30 end up?

Of the original $30, $25 went to the motel cash register. $1 to each guest. $2 to manager.

$25+$3+$2=$30

$30-$5=$25 total for room
$25/3 = $8.34 each for their room
$8.34 +$1 = $9.34 after $1 is returned
Add their portion of the tip to each: $9.34 + $2/3 = $9.34 + .66 = $10
3x$10 =$30

Damn, Fint. There is an easy way to resolve the problem that doesn't require division rounding.

You guys are a bunch of smartypantses.


There is. The math in my question is wrong. 3 x 9 is 27. Add the three dollars returned to get 30, not the two-dollar tip.

No way I'd stay in a $30 a night room, or is that hourly rate?. next question?

Wow, an oldie!

I first heard this from one of my Drill Instructors in 1974.

Thanks for the memory, Supe.

_

Oh I have many times, particularly in W Va. It was all good but I did bring my own pillow ! :D

The question seemed to be why his presumed net did not add up to the original amount. Had to show the net was not correct.

That comes out with the right answer, but only by happenstance.

The trick is in the line: at this point each traveler has paid $9.
Not true. They have paid $9.33

But you now know that.
Best
Les

I stand by my answer. It is exactly how you account for the full $30 after starting with 3 x 9. Not coincidental happenstance. My business card says "Statistician," Fint.

It is a riddle that initially eludes most people, though.

You need a new card. You did not account for the $2 and your net from each was incorrect. You lost a dollar on the net then add 3 twice which incorrectly makes up the dollar vice 3 and 2.

My card says scientist...but that doesn't allow me to create my own math.

Oh ya, well Tabs' card says "Tabs".

Beat that!

_

Your answer is correct.

Where did you account for the $2? Not even close.

To arrive at $27, you would have to have already included the $2 tip as part of the $9 each...and the additional 3 dollars would be the ones taken back (not the construct of the problem).

Sorta my point, they will put anything you want on a card. This is mine:

http://forums.pelicanparts.com/uploa...1636240072.JPG

Fint being Fint.
https://riddlesbrainteasers.com/missing-dollar/
There is no missing dollar from the original $30 because after getting $1 back, the three travelers had paid a total of $27 for their room ($9 each), not $30. Out of that $27, the hotel has $25 and the clerk kept the remaining $2. If you still want to work from the original $30, the travelers have $3, the hotel has $25 and the bellboy has $2. The misleading part is adding the bellboy’s $2 to the $27, when in fact it should be subtracted.

3 + 6 = 9

BUT

3 x 3 = 9

Where did the 6 go? Shouldn't it be 12?

Sooner being later:

That is not what the problem said or the answer posted. According to the problem, the $27 did not include the tip. That is where the dollar is lost n the original calculation...but not really lost.

" Three travelers stop at a motel and ask for a room. Manager says the room is $30 and they each pull out a $10 bill. Later, the manager comes to them with five $1 bills, and reporting he erred by charging them the weekday rate on a weekend when rooms are actually just $25. The travelers notice the five $1 bills cannot be evenly distributed among them, so they take each take $1, and the remaining $2 becomes a tip for the manager. At this moment, each traveler has paid a net amount of $9.

Three times nine is 27. Add the manager's tip and you have $29. Where did the remaining dollar go?"

There is no missing dollar. Only poor methodology.
25 in the cash register
2 bucks in the managers pocket.
3 bucks returned to the customers.
$30

You are marking this WAY too difficult.

Wow, this gang will argue about anything.

Snow tires!

Just making it accurate...and my answer was absolutely correct (unlike the other). Adding the 3 dollars twice (instead of 3 and 2) because of the earlier mistake is not the answer in the math.

The net was not $27 ($9 apiece) before the tip, it was $9.34 with the net of $28 That is where the original problem lost the dollar which was where the problem was. Then adding the tip gives you thirty.

Working a problem backwards to make it work once you have the answer is good if you know how to work the problem to start with. It does not work otherwise.

And as stated above, the inference that the tip to the manager should be add to the $27 is the misleading bit. That is classic misdirection.

Best
Les

Exactly. How one frame it to pocket the extra dollar....0r $1M if the problem is changed.

Exactly.

Sounds like govt accounting to me.

8.33 x 3 =.25

10 x 3 = 30

10 -1= 9

2 ÷ 3 = .66

9 + .66 = 9.66

Alright Tabs...you know that real math is not allowed in OT...and complaining about it is evil. Take it to PARF!

Three guys give up $10 each to pay $30. $5 is refunded as an overpayment Each keeps $1 for a total outlay of $9 each. 9 x 3 = 27. They give the leftover $2 back as a tip. (9 x 3) - 2 = 25.

In the riddle the $2 tip is being used twice to arrive at $29.

First time when it is applied to the actual $25 room charge to arrive at $27.
Second time when it is applied to the $27 to arrive at $29.

The $3 refund should be subtracted from the original payment of $30 to arrive at $27.

It's a clever shell game with words.

The real riddle is imprecise wording so y'all can argue on how frame the same simple kindergarten arithmetic in multiple ways.

no matter how the accounting, there is no extra dollar and there was never a reason to believe there was an extra dollar, so there is no correct way to frame said non existent dollar

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This old chestnut again, really?

Okay. You have nine coins, all identical in appearance, but one is lighter than the others. You have a simple balance scale that you can use two times to identify the lighter coin. Difference in weight is subtle enough that you can't tell the difference by holding the coins.

Go