Paradox!!!

[costargh]

Three people go to a hotel and rent a room, the room is 30 dollars for the night so they split it and pay 10 dollars each. After a while, the hotel owner remembers that he actually has a deal on tuesdays, that is 25 dollars for a room, and its tuesday, so he sends one of his staff members to go return the 5 dollars.

So he goes to return it, and the people who rented the room are happy that they were honest and didnt try to scam them, so they tip the staff member 2 dollars and they split the remaining 3 dollars between themselves, meaning they only spent 9 dollars each for the room.

So, they spent 9 dollars each, meaning they paid 27 dollars, and they gave the staff member a tip of 2 dollars, making the total to 29 dollars, Where did the last dollar go?

[dekoyl]

Each person (at the end) ends up with $1.
The staff has 2 dollars.
The hotel owner has  25 dollars.

3x1 =3 + 2 =5 + 25 = 30.

Easily seen if one person is said to have ONLY $10 and they spend it ALL.
-------------------
A: $10, B: $10, C:$10
"Okay we give you all our money. We now all have $0 each."
"Yay. I got $30. But today is special day. I give back $5. So I now have $25".
"Okay. $5 is split between 3 guys. But they give the staff $2. So they have $3 to split between each guy."
"$1 for you, $1 for you, $1 for me."

25 + 2 + 1 + 1 + 1 = 30
-------------------
Did I interpret the question wrong?

------------------
Ah, I see what this question is about. Sorry costa, I'm not good enough to work out the cause of this missing $1.

[costargh]

I can obviously work out what you've just shown, but why doesnt it work the other way.

3 * (10 -1) + 2 = 29?  

edit: reading the rest of your post now!

[shinny]

Three people go to a hotel and rent a room, the room is 30 dollars for the night so they split it and pay 10 dollars each. After a while, the hotel owner remembers that he actually has a deal on tuesdays, that is 25 dollars for a room, and its tuesday, so he sends one of his staff members to go return the 5 dollars.

So he goes to return it, and the people who rented the room are happy that they were honest and didnt try to scam them, so they tip the staff member 2 dollars and they split the remaining 3 dollars between themselves, meaning they only spent 9 dollars each for the room.

So, they spent 9 dollars each, meaning they paid 27 dollars, and they gave the staff member a tip of 2 dollars, making the total to 29 dollars, Where did the last dollar go?

Whited out for those who want to try work it out themselves. Highlight if you want (embarassing if I got it wrong though  :buck2:).
The fallacy lies in the bolded statement. The $27 stated includes the tip of $2; it is not an additional expense. Therefore, the 'system' if you will, now only has $27 within it, of which $25 went to the hotel owner from the initial transaction, and $2 goes to the staff member. Remember that each guy already got $1 back to keep, so the total can't be $30, and there is no 'last dollar'.

[bucket]

But they spent 9 dollars each on the room. 3x10=30 spent - 3 dollars returned = 27 dollars spent. then they gave the staff 2 dollars, making the total spent 29 dollars.
This thing works if you think of it sort of 'backwards' like you did but not when you think of it in the order that I did.
Shinny the 27 doesnt include the tip... because after they get 3 dollars back they have spent 27 dollars only then they tip 2 dollars.

[shinny]

But they spent 9 dollars each on the room. 3x10=30 spent - 3 dollars returned = 27 dollars spent. then they gave the staff 2 dollars, making the total spent 29 dollars.
This thing works if you think of it sort of 'backwards' like you did but not when you think of it in the order that I did.
Shinny the 27 doesnt include the tip... because after they get 3 dollars back they have spent 27 dollars only then they tip 2 dollars.

Your mistake is in your first line. It was $5 returned; not $3.

[qshyrn]

i think everyones confused by this... but its easy if you break it down.

so they get 5 bucks back after paying 30, meaning they paid only 25
they give back 2 bucks, meaning they pay 27 now. -- YOU DONT ADD 2 TO THE 27  its already included after 25+2!!!
They then get 1 dollar of each of the 3 dollars remaining...

[humph]

Another explanation below.

They give him $30. So they have each spent $10.
He gives them back $5. So they have each now spent $8.33, and have 3x$1.66 change.
They each take $1 of that share for themselves, and spend $0.66 as a tip.
So for each person:
$8.33 on the room
$0.66 on the tip
$1 change
adds up to $10 each...


I've definitely seen this on another forum somewhere...

[Mao]

nono. Wrong interpretation.

It need to be understood that the direction of change of money need to be the same for the addition to be valid. Hence the money spent by customers + money gained by staff does not have a real meaning. It's the same as saying "I have spent $20 today, and I have earnt $50 today, together that is $70", which has absolutely no real meaning at all.

Hence the only real equation is , i.e. 3*(-9) + 2 + 25 = 0, which is true.

[shinny]

nono. Wrong interpretation.

It need to be understood that the direction of change of money need to be the same for the addition to be valid. Hence the money spent by customers + money gained by staff does not have a real meaning. It's the same as saying "I have spent $20 today, and I have earnt $50 today, together that is $70", which has absolutely no real meaning at all.

Hence the only real equation is , i.e. 3*(-7) + 2 + 25 = 0, which is true.

I assume you mean -9 =P But yeh, to my understanding, it's not even a case of directionality. It's just that the $2 was included in the $27 to begin with in the question stem. That's like saying, I spent $20 today, of which $5 was on cake. Therefore I have spent $25 today.

[bucket]

Hey, I know I probably shouldn't ask this here but... wtf is with the top few 'applauded' users? Been some real ass licking going on?

[costargh]

I HAVE READ EVERYOENS REASONINGS ABOVE... CAN SOMEONE EXPLAIN WHY THIS ISNT RIGHT??? HAHA I KNOW IT ISNT BUT I STILL DONT GET IT. 24 METHODS, I KNOW LOL

But ... Person A, B and C had $10 each, ....

after paying a combined $30 each they had $0 left each

after getting $5 back they each had like $1.6666666 right?

and now they give the staff member a combined $2 (aprox .666666c each) so each is left with $1....? So $10 less $1 each= $9 each X 3 = 27 + 2 = 29???


i feel shit haha

[Mao]

Another explanation below.

They give him $30. So they have each spent $10.
He gives them back $5. So they have each now spent $8.33, and have 3x$1.66 change.
They each take $1 of that share for themselves, and spend $0.66 as a tip.
So for each person:
$8.33 on the room
$0.66 on the tip
$1 change
adds up to $10 each...


I've definitely seen this on another forum somewhere...

I disagree. The $10 and $8.33 afterwards is their 'stake' in the hotel room, which is held by the manager. They then further invest $0.66 each in the staff member, spending a total of $9, and having $1 as cash.

i.e. the $9 they paid includes the hotel room and the tip. the $1 each is left as unspent money. The misconception here is the addition of total money spent with the tip given.

[dekoyl]

I HAVE READ EVERYOENS REASONINGS ABOVE... CAN SOMEONE EXPLAIN WHY THIS ISNT RIGHT??? HAHA I KNOW IT ISNT BUT I STILL DONT GET IT. 24 METHODS, I KNOW LOL

But ... Person A, B and C had $10 each, ....

after paying a combined $30 each they had $0 left each

after getting $5 back they each had like $1.6666666 right?

and now they give the staff member a combined $2 (aprox .666666c each) so each is left with $1....? So $10 less $1 each= $9 each X 3 = 27 + 2 = 29???


i feel shit haha

I just think there's a gap that needs to be leaped over

Yes, each person now has $1 after giving the staff $2 in total.
So $3 is left with the guys.
$2 is with the staff.
$25 is at the front desk.
There's still $30 in the system.

[shinny]

Another explanation below.

They give him $30. So they have each spent $10.
He gives them back $5. So they have each now spent $8.33, and have 3x$1.66 change.
They each take $1 of that share for themselves, and spend $0.66 as a tip.
So for each person:
$8.33 on the room
$0.66 on the tip
$1 change
adds up to $10 each...


I've definitely seen this on another forum somewhere...

I disagree. The $10 and $8.33 afterwards is their 'stake' in the hotel room, which is held by the manager. They then further invest $0.66 each in the staff member, spending a total of $9, and having $1 as cash.

i.e. the $9 they paid includes the hotel room and the tip. the $1 each is left as unspent money.

What he has there isn't wrong. He just hasn't laid it out as you'd like it. His way of looking at it is still perfectly valid as far as I can see as the numbers regarding where the money went are all correct.