This Will Mess Up Your Head‏!

[Rami_s]

3 MEN GO INTO A HOTEL.

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?

[Tawa]

Each Guy Payed 9$ ~> 27$, Which Is Equal To 25$ Room Price And 2$ For The Boy.
Ye3neh First They Payed 10$ Each, Then They Got 1$ Back, So Each One Payed 9$.

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.

This Is Where You're Mistaken, It's 27$ In Total + The 3$ They Got Back.
Which Is 30$

Where's The Messing Our Head Part?

[xcoder]

It's logical but somehow tricky.
30-3=27$ equal to 9x3=27$ that includes the tips!
so the 9$ paid by each includes 1/3 of 2$ of the tips given to the boy

[KeXasthur]

These are not really "math calculative logical problems" .They are just meant to make you think about something by using some certain chronology in the problem, right use of words, and reversible thinking.

The two dollars that the bellboy kept should not be considered when talking about the whole amount that they eventually payed, but included in the calculation of the whole amount he should have distributed to each. That is because you said he couldn't split them evenly which means you can't use that 2 dollars anymore.

Which means the 2 dollars the bellboy kept were out of the 30, which makes it 28 dollars left ( notice the word "left" ). Now, divide 28 over the three of the guys since that is what they payed altogether, you get 9.333333. So each payed 9.333333, that is because the 25 they should have payed is what you should take into consideration, not the 30 they payed. It's just playing on words going on here. To verify: 25 ( what they should have payed) + 3 dollars ( which they got back out of the 5 ) makes 28, and now the 2 dollars the bellboy kept, that is 30 altogether.
Before they got their money back, each payed 9.333333 which is 30 minus the 2 dollars the bellboy kept. So eventually with each being given a dollar back, 9.333333-1= 8.333333 which is the number of dollars each guy payed, when the bellboy gave them the money back.

Tawa summed it in few words, that is because this is not mathematical; this is only playing with the words, and deducing stuff out of stuff that you already deduced off, but I thought I could just could put it into numbers.

[KeXasthur]

In even different way of putting it out, consider this:
30 is the number they ACTUALLY payed first.
25 is the number they SHOULD have paid.
BUT what actually happened is that eventually they payed 28
... and 28 is the number they ACTUALLY paid in the end.
The problem disregarded this chronology when actually asking you the problem.
So, to put it in simpler way

-with the 30, each payed 10 at first.

-with the 25, each WOULD have paid 8.333333 because 30-25 =5 ; 5/3= 1.666666
which means 10 ( what each payed first) - 1.666666 ( what should have been discounted) = 8.333333 is the number they should have payed if the bellboy wanted to distribute it fairly and not keep money with him, but that is NOT what happened.

-with the 28 ; 30- 28 = 2. That 2 dollars IS THE ACTUAL NUMBER they were exempted from paying. So divide this 2 dollars over the 3 of them. 2/3 = 0.666666. That 0.666666 number is the number each of them was exempted from actually paying in the end. So 10 -0.666666= 9.333333, which is the number that each of them ACTUALLY payed in the end. To relate it to the above, 1.666666 - 1 ( which is the number each "got back") = 0.666666 ( notice the quotations in "got back" , and read the lower conclusion)

Even in shorter, the bellboy would have given them money if you want to compare it to the 30 they originally payed, but he actually took away money from them compared to the 25 they SHOULD have payed.
So the three dollars he gave back to them in total doesn't have to do with the 30 but rather the 25. So, you don't subtract the 3 from the 30, but actually add the 3 to the 25.

I hope that was clearer than the above.

[Tawa]

This Is Already Posted By The Way.