3 people go go a hotel. They are charged $30 at the desk. They each
chip in $10 and go up to their rooms (this was a long time ago when
rooms were cheap). The hotel manager then remembers that there is a
special, and 3 rooms rent for only $25. So he gives the bellhop 5, $1
bills to take to the people. He gives $1 to each of them, and he keeps
2 (as a tip). Each of the 3 had then paid 10-1 = $9 for the room. 3 x
9 = $27, plus the two the bellhop kept makes $29. What happened to the
last dollar? ...

Looking at this from another way, each of the people paid $9.666.. , 9
for the room plus one third of $2. But 3 x 9.66.. is not 10, and there sure
as heck are 30 real whole dollars to account for.

What gives??

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Request for Question Clarification by rainbow-ga on 24 Feb 2006 11:59 PST

Does this explanation answer your question?

"The facts in this riddle are clear: There is an initial $30 charge.
It should have been $25, so $5 must be returned and accounted for. $3
is given to the 3 friends, $2 is kept by the bellhop - there you have
the $5. The trick to this riddle is that the addition and subtraction
are done at the wrong times to misdirect your thinking - and quite
successfully for most. Each of the 3 friends did indeed pay $9, not
$10, and as far as the friends are concerned, they paid $27 for the
night. But we know that the clerk will tell us that they were charged
only $25 and when you add the $3 returned with the $2 kept by the
bellhop, you come up with $30."

The Missing Dollar Riddle
http://www.justriddlesandmore.com/missingsol.html

Regards,
Rainbow

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Clarification of Question by jbritton-ga on 01 Mar 2006 05:47 PST

I like the canadianhelper's lead to the previous answers to this
question. After reading them, I now understand the solution. Thanks.

Or...just search Google Answers! Question asked and answered here:

http://answers.google.com/answers/threadview?id=468721

This one always gets people. The easiest way of disentangling it for
yourself is first of all to forget about the "three men", which is
simply a red herring - think of just one man. Then forget about the
"special", another red herring - assume the price of the room was $25
from the off. So the man gives the manager $30 dollars, the manager
gives him $5 change, and the man gives $2 of the change to the bellhop
as a tip. Where's the puzzle? As Rainbow says, this is a great example
of mental misdirection, corresponding to the visual misdirection used
by stage magicians.

I find this similar to the Exchage Rate problem I have with customers
at the bank I work for...

Customer....I saw on the news today that the Canadian dollar is worth
.86 American...so it should only cost my 1.14 to get an American
dollar right?

Me...No..you are using subtraction instead of division....it will cost
you 1/.86 which is 1.1627 NOT 1.14

The 'trick' is in realizing when to use subtraction and when to use division.