# Math Help - 3 guys go to a Hotel

1. ## 3 guys go to a Hotel

i was asked this puzzle today
three guys go to a hotel the man there says its 30$a nite so they each give him 10$
then the man comes back to them and says i made a mistake its 25$a night he gives each of them 1$ back and says i can't make change for the last 2$so they each payed 9$ 3x9 is 27 plus the 2 the man kept is 29 where is the other dollar to make 30$and or way does the math work one way and not this way i know there is something i don't get or do not know of so take it ez on im an old guy 2. If $x=\sqrt{2}$ then $x\not= \pi$. That is the nonsense of this question. 3. One of the silliest/oldest puzzle; google "Missing dollar riddle". 4. Originally Posted by toren i was asked this puzzle today three guys go to a hotel the man there says its 30$ a nite so they each give him 10$then the man comes back to them and says i made a mistake its 25$ a night he gives each of them 1$back and says i can't make change for the last 2$ so they each payed 9$3x9 is 27 plus the 2 the man kept is 29 where is the other dollar to make 30$ and or way does the math work one way and not this way
i know there is something i don't get or do not know of so take it ez on im an old guy
I have heard this puzzle before but thinking about it right now the $2 which we add is included in the$9 spent by the three person and it does not fit with the remainder of the $10. The puzzle by itself misleading us to add the$2 from which it is made out off.

5. Originally Posted by sgguhan
The puzzle by itself misleading ......
Well, if it wasn't misleading, then it wouldn't be a "puzzle", right?

6. Originally Posted by Plato
If $x=\sqrt{2}$ then $x\not= \pi$.
That is the nonsense of this question.
Haha, indeed. I like the confusion it creates, though.

7. ## Re: 3 guys go to a Hotel

How come nobody is adding the dollar each man has in his pocket?

Each man paid 9, the bellhop has 2, each man has a dollar, total... 32 dollars!

8. ## Re: 3 guys go to a Hotel

OK, I'll be a bit serious... no, it's not easy for me

As others have said, this is a pretty famous problem, and you may well have already Googled the solution. The answer is that the numbers are added incorrectly.
But the numbers are fine. Consider: when all is said and done, the room is $25. They tipped the bellhop$2. $25 plus$2 is the $27 total paid, or$9 per man.

Suppose the bellhop had made a really big error and said the room is $16 per night, not$30. Okay, so he gives each man $4 back, and says I cannot make change for the$2 i have left. They let him keep it.
Using these numbers, the problem would have been worded something like:
"So each man paid $6.$6x3 is $18 plus the$2 the bellhop kept, which is $20. Where is the missing$10 to make $30?" ...and that question will likely be pondered far less. A much bigger error causes one to consider sooner that something is amiss. The problem has stuck since the "difference" using this funny reasoning and the numbers it does is only$1. When it gets bigger than that, as it just did when we used different numbers, the faulty addition is easier to see...

9. ## Re: 3 guys go to a Hotel

Originally Posted by mathbyte
OK, I'll be a bit serious... no, it's not easy for me

As others have said, this is a pretty famous problem, and you may well have already Googled the solution. The answer is that the numbers are added incorrectly.
But the numbers are fine. Consider: when all is said and done, the room is $25. They tipped the bellhop$2. $25 plus$2 is the $27 total paid, or$9 per man.

Suppose the bellhop had made a really big error and said the room is $16 per night, not$30. Okay, so he gives each man $4 back, and says I cannot make change for the$2 i have left. They let him keep it.
Using these numbers, the problem would have been worded something like:
"So each man paid $6.$6x3 is $18 plus the$2 the bellhop kept, which is $20. Where is the missing$10 to make $30?" ...and that question will likely be pondered far less. A much bigger error causes one to consider sooner that something is amiss. The problem has stuck since the "difference" using this funny reasoning and the numbers it does is only$1. When it gets bigger than that, as it just did when we used different numbers, the faulty addition is easier to see...
Yeah, but each man has $4 in his pocket... making the total$32...AGAIN!

10. ## Re: 3 guys go to a Hotel

Originally Posted by agentmulder
Yeah, but each man has $4 in his pocket... making the total$32...AGAIN!

Sure... "that" way of adding it will always be $32.$30 plus $2 is always$32. If one starts running the numbers:

$30 paid,$1 each given back from the bellhop:
$9 each plus$1 each in their pocket plus $2 to the bellhop: = 27+3+2 =32$30 paid, $2 each given back from the bellhop:$8 each plus $2 each in their pocket plus$2 to the bellhop: = 24+6+2 =32

$30 paid,$3 each given back from the bellhop:
$7 each plus$3 each in their pocket plus $2 to the bellhop: = 21+9+2 =32$30 paid, $4 each given back from the bellhop:$6 each plus $4 each in their pocket plus$2 to the bellhop: = 18+12+2 =32

and so on.

In other words, where

r=room rate
c=change given back