Where did the dollar go?

[Ceritus]

Ok, this is something fun and I am to dumb to explain why it happens but this is the little riddle.

3 women go to a hotel clerk wanting a room. the clerk says it will be $30 for a room so each woman hands over $10.

The women go to the room and are hanging out then the clerk notices that the room is only $25 so he call the bell boy over and hands him $5 in $1 dollar bills to go refund the women their money.

The bell boy gets to the room and cannot figure out how to split the $5 amongst 3 women so he gives each woman a dollar and keeps 2 for himself.

If each woman is refunded a dollar it means each woman only paid $9 for the room which = $27 and the bell boy kept $2 which equals a total of $29. Where is the missing dollar?

 

[GreedyAlgorithm]

Um, aren't you forgetting something? The real thing to note here is that $27 was paid, minus $9 average payment, plus the $5 discount, gives a total of 23 dollars.

23

 

[Baron Samedi]

The women paid $27, which is $25 to the hotel and $2 to the bell boy. The women received back $3. 25 + 2 + 3 = 30, so there's no missing dollar.

 

[Ceritus]

The women paid $27, which is $25 to the hotel and $2 to the bell boy. The women received back $3. 25 + 2 + 3 = 30, so there's no missing dollar.

No the women paid $27 for the room in their minds since they were only refunded the $1 each and the bell boy kept $2. which is still $29


10 - 1 = 9

10 - 1 = 9 = 27 +$2 the bellboy stole = $29

10 - 1 = 9

 

[Ceritus]

Um, aren't you forgetting something? The real thing to note here is that $27 was paid, minus $9 average payment, plus the $5 discount, gives a total of 23 dollars.

23

$30 was paid originally, 5 was subtracted because of a clerical error. The woman recieved $1 back each because of the error and the bellboy stole $2 so the women each paid $9 which equals to $27 the bell boy stole $2 which equals to $29 spent. Yet $30 was spent originally there is a missing dollar.

There are no assumptions each woman paid $10 to begin with. Each woman recieved $1 back so each woman ended up paying 9$ and the bellboy stole $2. Which only equals $29

 

[pvt1863]

The problem is that $2 of the bill is accounted for twice. The women think they paid $9 each, and that includes the $2 to the bell boy. To say they paid $9 each for the room and $2 to the bell boy counts this $2 twice.

So the women paid $27 total (not $29) and got $3 back. That is $30.

To be very specific, each woman paid $25/3 = $8.33 each for the room, $2/3 = $0.66 each for the bell boy, and each got $1 back. So the total is 3*($8.33 + $0.66 + $1) = $30.

Not knowing that the bell boy took $2, they each think they spent $9 for the room and each got $1 back. So the total as they know it is 3*($9 + $1) = $30.

 

[CapelDodger]

If each woman is refunded a dollar it means each woman only paid $9 for the room which = $27 and the bell boy kept $2 which equals a total of $29. Where is the missing dollar?

There was one bell-boy. Add the one to the 29, and there's your 30 .

 

[cyborg]

It's this sort of trickery that con artists engage in.

The women paid $27 for a $25 room. The difference was kept by the bellboy - 2$.

No money was lost. You have been persuaded by a trick of language to think otherwise.

 

[The Whether Man]

That's the problem with employee pilferage. It would have been better for the bellboy to give the women the five dollars, and let them tip him. Then the women would see that they each paid $8.33 1/3 each for the room, not $9 or $10.

 

[CapelDodger]

The problem is that $2 of the bill is accounted for twice.

The problem is that the 27 they've paid and the 2 the guy's got don't add to anything meaningful. It's not made more meaningful by there being another number in the story which is close to it.

$27 dollars was paid : 25 are in the till, 2 are in Jack's pocket, 25+2=27, all accounted for. That's a meaningful sum and equation. This "27+2" nonsense isn't.

 

[Ceritus]

There was one bell-boy. Add the one to the 29, and there's your 30 .

Lol what the heck! Bellboys are not currency.

I keep falling short understanding it because $30 was spent originally now only $29 is totally spent.


Look at it this way would a dollar be saved if they originally paid $9 a peice and tipped the bell boy $2 for a $27 dollar room?

 

[Jimbo07]

Ceritus,

read peoples' posts! You don't get anything back (except for an accounting error) by re-adding the $2 to the $27.

 

[Rob Lister]

the bellboy made his tip with the massage

 

[Ceritus]

Hahaha I get it now.

 

[CapelDodger]

Lol what the heck! Bellboys are not currency.

So what? You tell a story with numbers in it, pluck out two and add them, then point out that the sum isn't the same as a third. Why would it be? So I just take out another number - one, as in the bellboy count - and spuriously explain the difference.

I keep falling short understanding it because $30 was spent originally now only $29 is totally spent.

The 29 is the sum of what was spent (27) plus the 2 that Jack kept. That's not what was so totally spent, it's a meaningless figure. Signifying nothing.

 

[Jeremy]

Women entered hotel. Clerk- 0 BB- 0 Women- 30
The women paid 30 to the clerk. Clerk-30 BB-0 Women- 0
The clerk gave five to the BB. Clerk- 25 BB-5 Women- 0
The bell boy gave 3 to the women. Clerk- 25 BB- 2 Women- 3

25+2+3=30

A 25 dollar room divided between 3 women = 8 1/3
2 dollar "tip" split between 3 women = 2/3
8 1/3 +2/3= 9 dollars paid.
9 dollars per woman = 27 (room + "tip")

The secret lies in that the women did not pay 27 dollars for the room, but for the room and the Bell Boy. You don't add the stolen 2$ because it is part of the 27.

EDIT: Must of taken too long in formatting it; Ceritus has already seen the error of his ways.

 

[Just thinking]

Look how things go awry when we keep the language the same and change the numbers ...

Three women pay $30 (together) for a room.
The manager claims it should only cost $21 and tells the room clerk to refund the difference.
He gives each only $1 -- and pockets $6.
Each thinks they paid $9.
Now ... $9 x 3 = $27 ... plus the $6 the clerk kept = $33.
Where did the extra $3 come from?

This should show that what they believe they paid is a meaningless statement, for if the room was only $10 and the clerk never gave back a dime, we would find a discrepancy of $20 too much. One can only look at what they truly paid as a result of what the room truly cost and then divvy up the refund not just among the women, but the clerk as well -- for he is now becoming involved in the refund, whether it's to their knowledge or not.

 

[RandFan]

You are counting the $2 twice. You can't do that. You can't add $2 to $27 because it is already part of the $27 ($25 + $2 = $27).

Q: How much does the hotel have? A: $25.

Q: How much does the bellboy have? A: $2

Q: How much in change did the women get back? A: $3.

$25 + $2 + $3 = $30. It works every time. You just need stop trying to add the $2 back to the $27 since that is nonsensical.

 

[GregC]

I'm surprised that no one had the real answer:

The next night two men went to the same hotel and got a room for $15 (near the ice machine.) Each paid $7.50. The clerk realizes it was only a ten dollar room and gave the same bellboy $5 to bring to the men. The bellboy pocketed $3 and gave the men each back a dollar. Now each had paid $6.50 each. $6.50 + $6.50 = $13.00 + $3.00 the bellboy kept = $16.00. There's the missing dollar.

Meanwhile the bellboy was fired for stealling and the hotel went out of business because they weren't charging enough.

 

[steve s]

Regarding the OP, I heard that one on the radio many years ago. The two people hosting the show couldn't figure it out. Out of about a dozen people who called in only two got the right answer. And even after being given the right answer the two hosts couldn't understand that it was the correct answer. It was pretty frustrating. I was in my car shouting "You idiots!" at the radio.

Steve S.