Paradox!!!

[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

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.

Lol i think your missing the point... the point of the question is to show why working it out in a fashion displayed at the end of the question (or similarly as I have in my last post) doest not yield the same answer as the way you have shown it.

[qshyrn]

But then I don't get it..
My name is Billy, I'm one of the three men.
I just spent $10 on a hotel room, and a few hours later, I'm given back $1.
Hence, I've only spent $9, and so has my roommates Willy and Steve.
$9 + $9 + $9 + $2tip + ? = $30

you arent given back 1 dollar, ur given back 5/3 dollars

[humph]

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?

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.

You're right, really; Costa's misunderstanding is based on the fact that he's adding 27 + 2 = 29, whereas he should note that the tip has already been paid.

So Costa: they each spend $8.33 each on the room ($25 in total), $0.66 on the tip ($2 in total), meaning they have spent $9 each ($27 in total) on the hotel and tip. They each have $1 change ($3 in total).

[costargh]

Lol I just got it

[kamil9876]

heh old one

Here is a fave:

Frog is much faster than Turtle. They decide to have a race. Frog decides to give Turtle a headstart and it is assumed they will run at a constant speed. Turtle argues that no matter how long the racetrack is, he will win, his argument is as follows:

"Say I start at point A, by the time you will get to point A I will be at some point B, which is further away. By the time you get to point B I will by at point C. By the time you get to point C I will be at point D... ad infinitum, therefore you will never overtake me."

[shinny]

Lol i think your missing the point... the point of the question is to show why working it out in a fashion displayed at the end of the question (or similarly as I have in my last post) doest not yield the same answer as the way you have shown it.

Tried to show that in "The $27 stated includes the tip of $2; it is not an additional expense" and "That's like saying, I spent $20 today, of which $5 was on cake. Therefore I have spent $25 today", because the latter sentence is basically what the question stem is saying. Perhaps I didn't explain myself well enough =\

[costargh]

Lol i think your missing the point... the point of the question is to show why working it out in a fashion displayed at the end of the question (or similarly as I have in my last post) doest not yield the same answer as the way you have shown it.

Tried to show that in "The $27 stated includes the tip of $2; it is not an additional expense" and "That's like saying, I spent $20 today, of which $5 was on cake. Therefore I have spent $25 today", because the latter sentence is basically what the question stem is saying. Perhaps I didn't explain myself well enough =\

Obviously not well enough for someone with a shit math brain like me

[humph]

heh old one

Here is a fave:

Frog is much faster than Turtle. They decide to have a race. Frog decides to give Turtle a headstart and it is assumed they will run at a constant speed. Turtle argues that no matter how long the racetrack is, he will win, his argument is as follows:

"Say I start at point A, by the time you will get to point A I will be at some point B, which is further away. By the time you get to point B I will by at point C. By the time you get to point C I will be at point D... ad infinitum, therefore you will never overtake me."

Zeno's paradox on Achilles and the tortoise, eh? The problem being that the ancient Greeks weren't really good with the idea of a limit...

My favourite paradox is the Banach-Tarski paradox

[/0]

I like Hilbert's Grand Hotel paradox. It's simple but crazy.

[Collin Li]

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?

I'm not sure how resolved this already is - but they came in with $30. $25 went to the hotel, $2 went to the tips and $3 went back to themselves.

They spent $27, that's right. You don't count the $2 tip again because that's already included (outgoing cashflows: 27 = 25 + 2), then $3 (30-27) change from their "$30 bill" is redistributed amongst themselves.


If you treat this like a chemical engineer treats transport processes (balanced mass flows, energy flows, etc.), or like an accountant treats cash flows (probably the more relevant analogy):

Cashflow balance for group
out: $30
return: $-5
tips: $2
net cost: $27 (don't add +2 AGAIN)

Where did that $27 go?
$25 hotel
$2 tips

It's wrong to see it like "27 + 2 + 1(?)"
The "remaining last dollar" was remaining three dollars (one in each pocket).

[lachymm]

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?

I'm not sure how resolved this already is - but they came in with $30. $25 went to the hotel, $2 went to the tips and $3 went back to themselves.

They spent $27, that's right. You don't count the $2 tip again because that's already included (outgoing cashflows: 27 = 25 + 2), then $3 (30-27) change from their "$30 bill" is redistributed amongst themselves.


If you treat this like a chemical engineer treats transport processes (balanced mass flows, energy flows, etc.), or like an accountant treats cash flows (probably the more relevant analogy):

Cashflow balance for group
out: $30
return: $-5
tips: $2
net cost: $27 (don't add +2 AGAIN)

Where did that $27 go?
$25 hotel
$2 tips

It's wrong to see it like "27 + 2 + 1(?)"
The "remaining last dollar" was remaining three dollars (one in each pocket).

Best explanation yet.

[brightsky]

Phase 1:

The three people give the hotel $30. Let's just assume that they ONLY have $30 in their pockets. So after the move, the three people have $0 between them and the hotel has $30.

Phase 2:

The hotel gives $5 back to the three people. Meaning that the three people now have $5 between them and the hotel has $25.

Phase 3:

The three people give the staff $2. Meaning that the three people now have $3 between them and the hotel has $25 and the staff has $2.

The quote "They spent 9 dollars each" incoorperates what they spent on the hotel as well as the staff member. And yeah, you don't count the tip of 2 dollars again. If you only count the money spent on the hotel, the three people would have spent a TOTAL of $25.

[TrueTears]

Here's one to think about:

A man stands 'a' meters from a wall.

He walks half the distance towards the wall so that he is now a/2 m away from it.

He then walks half the distance again towards the wall and now he is a/4 m away from it.

He then walks half the distance again and now he is a/8 m away from it.

But this can continue on forever since you can keep on halfing infinite times.

Which means this man will never reach the wall.

But from intuition ofcourse he will reach the wall.

Explain this paradox.

[brightsky]

Here's one to think about:

A man stands 'a' meters from a wall.

He walks half the distance towards the wall so that he is now a/2 m away from it.

He then walks half the distance again towards the wall and now he is a/4 m away from it.

He then walks half the distance again and now he is a/8 m away from it.

But this can continue on forever since you can keep on halfing infinite times.

Which means this man will never reach the wall.

But from intuition ofcourse he will reach the wall.

Explain this paradox.

Nice! I think it's just the same logic as how . As the number gets so small, or as it eventually gets to 0. Probably limits can explain this?

Edit out limit.

[TrueTears]

Here's one to think about:

A man stands 'a' meters from a wall.

He walks half the distance towards the wall so that he is now a/2 m away from it.

He then walks half the distance again towards the wall and now he is a/4 m away from it.

He then walks half the distance again and now he is a/8 m away from it.

But this can continue on forever since you can keep on halfing infinite times.

Which means this man will never reach the wall.

But from intuition ofcourse he will reach the wall.

Explain this paradox.

Nice! I think it's just the same logic as how . As the number gets so small, or as it eventually gets to 0. Probably limits can explain this?

Pro, you got it!

Limit the infinite geometric series!

('a' never approaches 0 it is constant, the denominator does)



Now what happens as 'n' approaches ?  :2funny: