This problem is driving me crazy!!!?

Question

3 MEN GO INTO A MOTEL.

THE MAN BEHIND THE DESK SAID THE ROOM IS $30, SO EACH MAN PAID $10 AND WENT TO THE ROOM.

A WHILE LATER THE MAN BEHIND THE DESK REALIZED THE ROOM WAS ONLY $25, SO HE SENT THE BELLBOY TO THE 3 GUYS' ROOM WITH $5.
ON THE WAY, THE BELLBOY COULDN'T FIGURE OUT HOW TO SPLIT $5 EVENLY
BETWEEN 3 MEN, SO HE GAVE EACH MAN A $1 AND KEPT THE OTHER $2 FOR HIMSELF.
THIS MEANT THAT THE 3 MEN EACH PAID $9 FOR THE ROOM, WHICH IS A TOTAL OF
$27, ADD THE $2 THAT THE BELLBOY KEPT = $29.
WHERE IS THE OTHER DOLLAR?

This is an email someone sent me and it is driving me nuts! Help!

Answer 1

This is just a trick question that can be solved logically using basic mathematics. Okay, so three men go into a motel and each pay $10 for a room, totalling $30. The actual price is $25. So the bellboy takes $5 in change to the three men to split up but gets confused. I suppose because he's immature, possibly going through a tough time with his divorce settlement and custody battle. He also probably has a problem with gingivitis on top of it all. But anyway, he decides to pocket $2 to save everyone some trouble and to maybe get a snack out of the vending machine for later since he has to work overtime trying to pay for his overpriced one-bedroom apartment in the Bronx. The other $3 is split among the three men, each obtaining $1. So, that means that they each paid $9, right? Well:

$30 to start with.
- $5 taken back to men
= $25 left
$5 taken back to men
- $3 given away
- $2 in pocket of bellboy
= $0! There is no extra dollar! It is a trick!

Answer 2

I've been seeing this 1 a lot lately.
Each man paid $10 but then got back $1 for a net of $9/man or $27 total.
The manager received $30 but gave back $5 for a net of $25.
The bellboy kept $2.
The 3 men paid $27. $25 went to the manager & $2 to the bellboy
$25+$2=$27 received by the manager & bellboy.
$9*3=$27 paid by the 3 men.

Answer 3

There are many variations where what the three men paid plus what the bellboy kept doesn't add up to $30. For example, suppose the room cost $22, so the bellboy went back to the room with $8, gave each man $2, and kept $2 for himself. Now the three men have paid $8 each, for a total of $24, and the busboy has $2, for a total of $26. Or suppose the room cost $4, the busboy took $26 to the room, paid each man $8, and kept $2 for himself. Now the three men have paid $2 each and the busboy has $2, for a total of $8. So the amounts don't have to add up $30; the example in the email just makes it sound like there's something funny going on because 29 is so close to 30.

Answer 4

This question actually has a hidden logical flaw that causes the confusion. To solve the mystery, consider my following claim:

Total output (by men) = Total input (to others)
That is, whatever the amount the three men gives out should be equalled to the sum of the amounts received by the other side.

Now, let's plug numbers into the equation:

$30 = $25 + $5 <- $30 given. $25 received, $5 surplus
$30 - $3 = $25 + $2 <- $3 paid back to men, $2 surplus
$27 = $25 + $2 <-- final result. $27 paid by men.
$25 to hotel, $2 to bell boy.
The equation is balanced (left side = right side)

now...observe from the above that "27" is OUTPUT, while "25" and "2" are INPUTS

remember the original equation: Total OUT = Total IN
if we rename the OUT and IN, we get:
(total paid by men) = (total received by hotel) + (bellboy $)

rearrange the equation, we get:
(total paid by men) - (bellboy $) = (total received by hotel)

the original question created confusion by ADDING together the two terms on the LEFT side of the above equation, when it should be SUBTRACTING.

The men paid $27. Since the bellboy kept $2, then effectively, $25 reached the hotel desk, which is correct. thus, the actual equation should be 27 - 2 = 25, NOT 27 + 2 = 29.

Answer 5

The $3 is back in the pockets of the men, no longer part of the equation. Each man paid $9 for the room, which is a total of $27, MINUS the $2 the bellboy kept, equals the $25 that the motel got for the room.

Answer 6

$30 is not what you should be looking for now. It should be $25

Let us represent this system using four variables: m1, m2, m3 and e, each representing the first man, the sencond man, the third man and the extra amount, respectively.

The presumed total at the beginning is $30. Remember, the prinicpal of this situation says that you can adjust each variable's value as long as m1+m2+m3+e is constant at 30.
m1=10
m2=10
m3=10
e=0

You can even represent the bellboy by e. Now you are free to distribute these value among the four variables as long as you don't violate the equation: m1+m2+m3+e=30.
There are infinite possible combinations for this. m1=8, m2=2, m3=16 and e= 4.

Nwow let us see the next step. Since the price is $25 and NOT $30, the former is what we should be looking for.
This is an important point:
Since the variable e represents the bellboy, any amount stored in it should be NEGATIVE as it is the amount OWED by the hotel to the men, and the equation we should be looking for now is:
m1+m2+m3+e=25, and not 30.
In step 1 (When the bellboy has the $5):
m1 = 10
m2 = 10
m3 = 10
e = -5
m1+m2+m3+e=25

In step 2(When the bellboy splits it unevenly):
m1 = 9
m2 = 9
m3 = 9
e = -2
m1+m2+m3+e=25 and NOT 29. You were getting a total of 29 since you were treating the variable e as positive, when it should not be. The apparent paradox in this question is just a problem with algebraic addition.

Answer 7

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.

Answer 8

There is no other dollar. The men paid 27 total. Bellboy got 2 man behind desk got 25. 27=25+2

Answer 9

The trick is the way you view the problem. Yes, the men paid a total of 9 dollars each for the room, a total of $27. But the room only cost $25. $25 of the $27 dollars went to the hotel, the other $2 went to the bellhop. Because the money was returned to the men, you only have to account for the $27 in circulation, not $30.

Answer 10

This is a very old puzzle. But it is a good one.
The 3 men each paid $9 to the hotel. ($25 went to the manager and $2 went to the bellboy) The other $3 is in the pockets of the 3 men.