Missing dollar riddle

[Dex]

Three guests check into a hotel. The Cashier says the bill is $30 so each pays $10. Later the cashier realizes the bill should only be $25. To rectify he gives the bellhop five singles to return to the guests. On the way back to the room the bellhop realizes that he cannot divide the money evenly. As they didn’t know the total of the revised bill, he decides to give each guest a dollar and keep two for himself.

Now that the guests have been given a dollar back, each has paid $9. Three times nine is 27 and the bellhop has $2. Two plus 27 is 29. If the guests originally handed over $30, what happened to the remaining dollar?

[grimey]

Nothing, it never existed (highlight below for answer).

Each guest paid $10. The cashier returned $5, so the total payment is now $25, not $30. $25/3 = $8.33, so each guest has now paid $8.33. The each get a dollar back, so they now have $8.33 paid, and $1 in pocket, for a total of $9.33 each, and $28 total. The bellhop has $2 for a total of $30.

[Dex]

Nothing, it never existed (highlight below for answer).
Each guest paid $10. The cashier returned $5, so the total payment is now $25, not $30. $25/3 = $8.33, so each guest has now paid $8.33. The each get a dollar back, so they now have $8.33 paid, and $1 in pocket, for a total of $9.33 each, and $28 total. The bellhop has $2 for a total of $30.[/color]

Just before each man received their dollar from the bellhop, each man was out 10 dollars from pocket. When they received their 1 dollar from the bell Hop that would make each man out 9 dollars from pocket. ... almost there.

[goates]

The problem is in the adding of the $2 the thief of a bellhop took. It should have been subtracted from the $27, not added.

[canwhitewolf]

dltd

[grimey]

No, my solution is correct. They each have 1 dollar in pocket, having paid 10 and gotten 1 back. The problem is that they paid $8.33 each for the room, not something else as your question implies. The missing dollar is the $0.33 cents that funky math didn't account for. There never was a missing dollar, the hotel has it.

3+(8.33*3)+2 = 30.

[goates]

No, my solution is correct. They each have 1 dollar in pocket, having paid 10 and gotten 1 back. The problem is that they paid $8.33 each for the room, not something else as your question implies. The missing dollar is the $0.33 cents that funky math didn't account for. There never was a missing dollar, the hotel has it.

Re-read the riddle. Each client paid $10 originally, for a total of $30. However, the price was meant to be $25 total, so they had collectively paid $5 too much. The bellhop gave them each $1 back, so they have now paid $9 each, when they should have only paid $8.33.

[grimey]

No, they each paid $8.33, and tipped the bellhop $0.66

8.33 + 1 + 0.66 = $10 (accounting for rounding the last cent)
$10 * 3 = $30.

There never was a missing dollar. The $2 the bellhop got is part of the $9, not in addition to it.

[Lurch]

Come on guys the government always get their share of the pot so they have the dollar

But seriously the math is wrong as stated by CWW

The guests paid a total of $27 (3 TIMES 9)

The hotel has $25

the bell hop has $2

25 + 2 = 27

They are messing with the math

Lurch

[BoostedNihilist]

the bellhop only ever has five dollars leaving the house with 25.. so at this point all 30 is accounted for..

Now, the bellhop takes 3 dollars and returns 1 to each guest leaving him with two (his tip)

3+2 =5
+25 = 30


25+3(guests)+2(el tipo or propina)=30


no missing dollar.

[niss]

The one dollar was a medical processing fee.

[Four1oh]

The one dollar was a medical processing fee.

fuel surcharge? :p Navcanada fee? Airport rent? GHAAA! where does it end?

[tvguru]

The power of the internet. I never have to use my brain! http://en.wikipedia.org/wiki/Missing_dollar_paradox

And there's always a video as well http://www.metacafe.com/watch/500323/wh ... ng_dollar/

[Topspin]

We unravel this confusion by recognizing that there is no reason to add $2 to $27. It should be subtracted.

The $3 amount that has been returned to the guests is a reduction in the amount that the guests paid, so it should be subtracted from the total. The bellhop returned $3 ($1 each), making their total payment $27 (mathematically, $30 - $3). Note that the $3 is subtracted from the total. If the bellhop then changed his mind and returned the additional $2 to the guests, it would also be subtracted from the total. The mistake is made in trying to add this $2 instead of subtracting it. Simple math demonstrates what readers intuitively sense, that there is no missing money. The sum of their payments is $25 in the till, $2 in the bellhop's pocket (totaling $27), plus the $3 in change that the guests now have, which brings the total up to $30.

The incorrect solution is: ($10 - $1) x 3 + $2 = $29. This equation is not meaningful: the number 29 is not significant to the problem, i.e. there is no "missing $1".

The correct solution is: ($10 - $1) x 3 - $2 = $25. In this case the solution is the bill amount, which is also the amount of money left in the till.

In other words, $27 is the amount that the guests have paid. Of that $27, $25 went into the till and $2 went to the bellhop. The other $3 is returned to the guests.

This problem provides a means to understand how misdirection, and irrelevant facts and questions, can foil clear analysis. Additionally, the tools used to resolve this paradox are used in the analysis of a wide range of financial and scientific areas.

[paddy]

Just don't stay a a hotel where the bill is $25. Probably a dump anyway.

[Dex]

TopSpin: You might want to reference your source in your post so people will not confuse the content as your own.