If then .
That is the nonsense of this question.
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
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...
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
you're adding:
3*r + 3*c +2
3*(r+c) +2
But, r+c is always 10. Thus,
3*(10)+2 = 32.
Still, that's what a to-remain-nameless former U.S. President would call "Fuzzy Math."