Ok,

Three men go to check into a hotel, and decide to share a room. They each give the hotel manager $10, for a total of $30. Then they proceed up into their room.

After they leave, the manager realizes he has overcharged them. The room only cost $25. So, he gives $5 to the bellboy, and tells him to bring the money to the men.

On the way to their room, the bellboy realizes he can not split $5 three ways, so he pockets two of the dollars, and gives each of the men one dollar.

Therefore, each of the men has paid $9 for the room. Three times 9 is 27. The bellboy kept two dollars...27 plus 2 is 29. Where is the thirtieth dollar?

I love this old one.

Argh! That made me head hurt. But there is no missing dollar. They paid $25 for the room and $2 for the fine services of the bellboy/thief. Therefore 9*3=27.

Therefore, each of the men has paid $9 for the room.

Uh, each of the men paid 28/3 = $9.33 for the room. Looks more like an exercise in careful reading than math...

Don't think so, Tudamorf. 25 dollars went to the inkeeper and 2 dollars went to the bell boy, that's 27 dollars.

"Looks more like an exercise in careful reading than math"

Both, really.

Panamah says: Don't think so, Tudamorf. 25 dollars went to the inkeeper and 2 dollars went to the bell boy, that's 27 dollars.

Bleh, my bad, I misread, it's 25/3 not 28/3.

So each of the men paid $25/3 = $8.33 for the room, they each got back $1, and the bellboy kept $2. 3 * $8.33 + 3 * $1 + $2 = $30, so I still don't see the "math" element of this riddle. It all makes perfect sense.

It's just a trick question, because it says "each man paid $9 for the room", when in fact they did not pay $9 for the room.

Actually, the men did each pay $9 for the room. They did in fact each pay out $10 and got one dollar back. If at the beginning of the story, each man had nothing but ten one dollar bills in his wallet, at the end, each would have one one dollar bill. By any stretch, they are paying 9 bucks each.

It's a math problem in the sense that it forces you to think about how this sort of thing works. Panamah nailed it.

Mappy says: They did in fact each pay out $10 and got one dollar back.

Yes.

Actually, the men did each pay $9 for the room.

No, because of the bellboy.

Why do you think those two statements are the same?

They each paid $8.33 for the room.

They each paid $0.66 for the bellboy.

They have 3 dollars left.

Sum is 30, there is no missing dollar any way you look at it. Saying they paid $9 for the room is just wrong, and that's where the question tries to fool you. If the $9 included the bellboy, then it shouldn't be added again.

This isn't really a math riddle. =/

[Edit] To make it clearer, if it weren't a trick question, it would read at the end:

"Therefore, each of the men has paid $8.33 for the room. Three times $8.33 is $25. The bellboy kept two dollars...25 plus 2 is 27. The three dollars are in each of their pockets."

the bellboy should have kept the 5 dollars and got a 6 pack and saves us all the headache :D

But then they couldn't have tipped the bell boy!

It all comes down to the wording of the puzzle

<blockquote><strong><em>Quote:</em></strong><hr>Therefore, each of the men has paid $9 for the room. Three times 9 is 27. The bellboy kept two dollars...27 plus 2 is 29. Where is the thirtieth dollar? [/quote]

This is really incorrect becuase the 3*$9 = $27 already includes the $2 paid to the bellboy, adding that figure in again and not mentioning the change given is what leads it astray.

Actually Tudamorf, you should be able to do the math using integers only. At no point did I describe people being giving pennies, nickles, or dimes...so no one is paying 8.33 or any other fractional amount in any sense. Only dollar bills are ever exchanged.

The men are paying $9 each, nine single dollar bills. The bellboy keeps two of those total 27 singles, and the manager is left with 25.

You don't count up from 27, you count DOWN from it...27 minus two is 25, which is what the hotel manager is charging. The point (if there is one) of the riddle is to figure out that you are not trying to get back to 30 at all. Yah the language is deliberately wrong, obviously so...29 of course doesn't equal 30. The trick is to figure out exactly WHY 29 doesn't equal 30, and the answer to that question doesn't involve fractions. Which is why it IS a math riddle, since you have to use mathmatical properties (what, associative, communative? I can't remember anymore) to logically solve it.

Actually Tudamorf, you should be able to do the math using integers only.

Yeah, but that wasn't my point. My point was that the "riddle" was about figuring out how the question lies to you, not in solving some sort of math problem. To demonstrate that, fractions are necessary, and I think the people reading this forum can understand fractions. It should really be called a word riddle, but then I guess that would give away the "trick".

It doesn't lie to you, it's a precedence problem, I think.

You can evaluate it like this:

9 * 3 = 27 + 2 = 29 oops

30 - 2 = 27 / 9 = 3 yay (3 guys bought the room)

25 + 2 + 3 = 30 yay (all accounted for)

30 - 3 = 27 - 2 = 25 Yay (cost of the room minus the tip)

30 - 2 = 27 / 9 = 3 yay (3 guys bought the room)


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Um... I may suck at this.. but 30 - 2 = 28.. not 27.


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Pay $30.
Cost $25.

Leftover $5 change.

Guy 1=gets $1
Guy 2=gets $1
Guy 3=gets $1
BellBoy= Gets $2

Leftover = 0, There is no lost dollar.

Each guy's part of bill = $8.333333333333333333333333
Each guy paid $10 and got $1 back = $9.
Each guy was still owed $0.6666666666666666666667

They three guys pooled their change of 0.666666 to give the bellhop a $2 tip.

To show the error of the example:

9 *3 +2 = 29.

It is the +2 that is wrong, it should be +3.

$9 * 3 = $27.. which equals what the guys paid for the room AND the bell boy. ($25 + $2).

Then you add in the $3 they got back as change. (They paid the Hotel $10, they spent $9... They get $1 back each).

I was up late!