Where did the last dollar go after the room was paid for?

Tendered: $30.00 (3 x $10)
less
Refunded: $ 5.00
Receipts : $25.00 ($8.3333etc x 3)

Given to women: $3.00 (3 x $1)
plus
Kept by bus boy: $2.00 ( $0.6666etc x 3)
Total of returns: $5.00


Receipts ..... : $25.00
plus
Refunded .... : $ 5.00 ($3.00 + $2.00)
Transaction : $30.00 (3 x $10.00)



The riddle's misdirection arises in that each woman's share of the $2.00 tip amounts to 1/3 of $2.00 (each tipped $0.66 plus the fractional cent required to total the $2.00); including tip each woman paid $9.33 (plus the fractional cent): $9.33333333 etc x 3 = $28.00, the busboy has $2.00, totaling $30.00, of which the motel keeper has $25.00

Where did the last dollar go after the rent was paid?
Thank you very much for the answer. That was really bothering me. Now I can share the answer with many others that were just as puzzled!Thanks again.

The answer timberlandko provided is wrong.

Here is how:

"The riddle's misdirection arises in that each woman's share of the $2.00 tip amounts to 1/3 of $2.00 (each tipped $0.66 plus the fractional cent required to total the $2.00); including tip each woman paid $9.33 (plus the fractional cent): $9.33333333 etc x 3 = $28.00, the busboy has $2.00, totaling $30.00, of which the motel keeper has $25.00"

NOTE this part: "including tip each woman paid $9.33" but then he also says "the busboy has $2.00, totaling $30.00"

You are following the author of this riddles logic. Which is incorrect, impossible math. You are adding a tip to a tip which doesn't exist. You say the 33 cents accounts for the tip but then you also say the busboy has $2.00 (which is the tip) so you are adding the tip to the tip.


Here let me state the question so that I can provide an answer:

***Three men go to a cheap motel, and the desk clerk charges them a sum of $30.00 for the night. The three of them split the cost ten dollars each. Later the manager comes over and tells the desk clerk that he overcharged the men, since the actual cost should have been $25.00. The manager gives the bellboy $5.00 and tells him to give it to the men. The bellboy, however, decides to cheat the men and pockets $2.00, giving each of the men only one dollar.
Now each man has paid $9.00 to stay for the night, and 3 x $9.00 = $27.00. The bellboy has pocketed $2.00. But $27.00 + $2.00 = $29.00. Where is the missing $1.00? ***

The answer for this question is i ( i in mathematics = imaginary number)
This is because the question faults its self in its english and its mathematics. Here is the fault, "Now each man has paid $9.00 to stay for the night" Each man does not pay $9.00 to stay for the night. Each man pays 1/3 of 25$ to stay for the night. Then, they also pay 1/3 of $2.00 each for the bellboy. You can't say they paid 27 dollars to stay for the night when they didn't pay 27 dollars to stay for the night. That is a contradiction.

But what you can say, is that the sum of the 30 dollars went in these directions:

Manager has $25 from the three men.
The three man have $3
The bellboy has $2

$25+$3+$2 adds up nicely to $30 which is correct math.
There is no vanishing dollar in this example.
But the question does not ask this. It gives an illogical story which cannot be solved. This is why I provided the answer to the riddle as i.

wrong again!
no, the answer jefflongoria provided is wrong too!

it's much more simple than that.

the answer... you're adding the $2 to the $27, when you should be subtracting to get the $25 that is the total amount in the till. the men paid $27: 25 for the room, and 2 to the bell boy.

the confusion is in the attempt to get the amount the bell boy has and the amount the women paid to get the total amount they paid in the first transaction. think of the women as one person - one person pays $30, is returned 3, so has paid 27. it's the 3 that was returned that should be added to the 27 to get 30. not the 2, which is involved in a different calculation - getting the 27 and the 2 to reach 25, which is the amount in the till.

the really interesting thing is figuring out why we so insistently think the 27 and the 2 should be added, and not subtracted. and i don't know why that is.

cathalcom is right, timberlandko and JeffLongoria are wrong. However, I find catholcom's explanation a bit confusing.

Here is how I would say it..

STEP 1
clerk: +30
woman 1: -10
woman 2: -10
woman 3: -10

STEP 2
clerk: -5 (to bus boy)
woman 1: +1
woman2: +1
woman3: +1
bus boy: +2

Now we add together the changes from steps 1 and 2 to get the net result.

NET RESULT
clerk: +25
woman1: -9
woman2: -9
woman3: -9
bus boy: +2

As you can see, the 3 women each each put in 9 dollars (27 dollars total)...of which 25 went to the clerk, and 2 went to the bellboy.

Re: wrong again!


We think it should be added because we were told it should be while our brain is still trying to process all the other complex misdirection.

It's similar to an old scam that grifters used to run. Buy a $1 item with a $20 bill. Then find another $1 to get a fiver instead of the 4 ones. Trade the two $5 for a ten. Then give the other ten to get the twenty back. Most clerks fail to spot the ten dollars they just lost.

Re: wrong again!


I'd ask why the hell he gave me a $20 to pay for a $1 item if he had a $1 bill handy.

http://www.able2know.com/forums/viewtopic.php?p=2519907&highlight=brother#2519907

Timber explained it nicely here.

Re: wrong again!


I'd be one of them because I can't see the catch.
You give me a 20 to buy a 1 dollar item.
I give you a 10, a 5, and 4 1's in change.
Then you give me 5 1's and I give you a 5.
You give me 2 5s and I give you a 10.
You give me 2 10's and I give you a 20.
Where's the catch? I don't see anything wrong with the above.

The clerk gives out a ten but then only gets the other ten back for the 20.

I still can't see it. I even made play money out of paper and it still works out fine.

The clerk gives the grifter a five. The grifter gives the five in his hand and the one he just got back to the clerk to get a ten. The clerk hands the grifter the ten. The grifter gives the other ten (only one) to the clerk and gets a twenty. The grifter pockets the ten the clerk gave him for the 2 fives.

Played correctly the clerk is so frustrated they don't immediately realize they already gave one ten and are only getting one back. If they do realize it the grifter admits to an "honest" mistake and gives both tens.

iono...i thinks its obvious something is wrong if u only receive one ten and r supposed to give out a 20

I find your explantion , is much better to read.