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Paradoxes


pureprayer

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Yeah, the easiest way to explain that goat/car thing to people who haven't heard it is to clarify that the host always opens a goat first, as well as for them to think of it as "would you rather pick one door, or two?".

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Got an interesting one.

 

 

 

There are three people staying in a hotel room. The bill is $30. They each split the bill and pay $10. The clerk notices the bill should of been $25 so he gives the bellhop the money to split. The bellhop cant split $5 three ways so he gives each person one dollar and two for himself.

 

 

 

BUT WAIT: Each person paid $9 for a room and the bellhop kept $2. 9*3+2= $29!?

 

 

 

Can anyone figure this one out?

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Got an interesting one.

 

 

 

There are three people staying in a hotel room. The bill is $30. They each split the bill and pay $10. The clerk notices the bill should of been $25 so he gives the bellhop the money to split. The bellhop cant split $5 three ways so he gives each person one dollar and two for himself.

 

 

 

BUT WAIT: Each person paid $9 for a room and the bellhop kept $2. 9*3+2= $29!?

 

 

 

Can anyone figure this one out?

 

10*3=30

 

30-5=25

 

25+3*1=28

 

28+2=30

 

 

 

It's just the order in which the math is done in your way.

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Got an interesting one.

 

 

 

There are three people staying in a hotel room. The bill is $30. They each split the bill and pay $10. The clerk notices the bill should of been $25 so he gives the bellhop the money to split. The bellhop cant split $5 three ways so he gives each person one dollar and two for himself.

 

 

 

BUT WAIT: Each person paid $9 for a room and the bellhop kept $2. 9*3+2= $29!?

 

 

 

Can anyone figure this one out?

 

???

 

The total for the room is 25, not 30. It should be: 9*3 - 2 = 25$ \'

 

 

 

A man has a locked box. He's seen a locksmith but he doesn't have the combination to unlock it. So he watches it, because at any moment it might show him what to take off the locks with so he chained himself to the box took a lock and then he locked it. Swallowed the combination and then forgot it. A man has a locked box. He's seen a locksmith but he doesn't have the combination to unlock it. So he watches it, because at any moment it might show him what to take off the locks with so he chained himself to the box took a lock and then he locked it. Swallowed the combination and then forgot it. A man has a locked box. He's seen a locksmith but he doesn't have the combination to unlock it. So he watches it, because at any moment it might show him what to take off the locks with so he chained himself to the box took a lock and then he locked it. Swallowed the combination and then forgot it.

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That's just rounding. 1/3 ? .333~ technically.

 

1/3 = .3333~..... all the way to infinity. But because it's infinite and all, the difference between the two is so small, that it's considered negligible and therefor considered the same.

 

 

 

for example the equation:

 

 

 

lim (8x³-9x²+17)/( 2x³-5x+12)

 

??

 

 

 

technically ='s nothing as ?/? is undefined.

 

But that is obviously not the answer.

 

You see, if you plug in very very large number close to infinity, such as 100000000 for x, you would get a number like 3.878787878 or something similar.

 

 

 

and if you plug in a number such as 10000000000000000000000 you would get something like 3.999999999888.

 

 

 

So if you were to keep going, the number you would get would start to get closer and closer to 4, which is the answer, because although the number was not exact, it's so close that it is indistinguishable.

 

Methinks someone should understand infinity if they know math this well.

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Just a little puzzle:

 

 

 

3 guys go to rent a hotel room, the room is $30, so they each pay $10. Later that night the hotel guy finds out the room is only $25 so he gives $5 to the bell boy to split between the 3 guys. The bellboy did not know how to split $5 in 3 ways so he kept $2 for himself and gave $1 to each guy so the guys only paid $9 a piece right? So if the guys paid $27 and the bellboy kept $2, where is the other dollar?

 

 

 

EDIT: Sorry, didn't see that pureprayer had posted this earlier.

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a=b

 

a^2=ab

 

2a^2=a^2+ab

 

2a^2-2ab=a^2+ab-2ab

 

2a^2-2ab=a^2-ab

 

2(a^2-ab)=1(a^2-ab)

 

2=1

 

 

 

Let's go through this step by step.

 

 

 

a=b Start

 

a^2=ab (times whole equation by a)

 

2a^2=a^2+ab (what the hell did you do here? You timesd the left side of the equation by a^2 and you added a^2 to the right hand side. You fail. It should be 2a^2=ba^3)

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A common one a friend pulls on me.

 

 

 

What happens when an Unstoppoble force that cannot change direction hits an unmovable, indestructive item?

 

 

 

It's a semantically contradictory statement. You can't have an unstoppable force if there exists an unmovable object and vice versa.

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A common one a friend pulls on me.

 

 

 

What happens when an Unstoppoble force that cannot change direction hits an unmovable, indestructive item?

 

 

 

It's a semantically contradictory statement. You can't have an unstoppable force if there exists an unmovable object and vice versa.

 

 

 

Paradoxes make my brain hurt like jelly in a massage chair. :cry:

 

 

 

Fun fact about that quote. The Chinese translation of "paradox" is actually an ancient reference to it. There's an infinitely powerful sword that will penetrate anything, and an infinitely resistant shield that can defend against anything. I remember my cousin's father telling me the story. :)

 

 

 

Oh, and about the Grandfather Paradox. Wouldn't you, having removed yourself from "your" present by time traveling, have made your new present become the time stream itself? Therefore, if you kill your grandfather, he's dead but you, existing in a time separate from your past present, are still alive and nothing changes (except for the fact that everyone who was born because of your grandfather don't exist in your past present). Thoughts on this?

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Why, when you look in a mirror, are you left-right inverted/flipped but not top-bottom?

 

 

 

The light that hits you and reflects onto the mirror does so in a straight line. Doesn't cross over to the other side of the mirror.

 

So light reflecting the right side of your face will appear on the right side of the mirror.

 

This gives a flipped image. You will raise your right hand, your mirror image will appear to raise 'his' left.

 

 

 

That makes sense to me. *Shrug*

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Why, when you look in a mirror, are you left-right inverted/flipped but not top-bottom?

 

 

 

The light that hits you and reflects onto the mirror does so in a straight line. Doesn't cross over to the other side of the mirror.

 

So light reflecting the right side of your face will appear on the right side of the mirror.

 

This gives a flipped image. You will raise your right hand, your mirror image will appear to raise 'his' left.

 

 

 

That makes sense to me. *Shrug*

 

 

 

If a point of an object has coordinates (-x, -y,z) then the image of this point (as reflected from the mirror in y, z plane) has coordinates (-x, y,z) - so mirror reflection is a reversal of the coordinate axis perpendicular to the mirror's surface. Thus, a mirror image does not have reversed right and left (or up and down), but rather reversed front and back.

 

 

 

Why does it do this? Specular reflection.

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That's just rounding. 1/3 ? .333~ technically.

 

1/3 = .3333~..... all the way to infinity. But because it's infinite and all, the difference between the two is so small, that it's considered negligible and therefor considered the same.

 

 

 

for example the equation:

 

 

 

lim (8x³-9x²+17)/( 2x³-5x+12)

 

??

 

 

 

technically ='s nothing as ?/? is undefined.

 

But that is obviously not the answer.

 

You see, if you plug in very very large number close to infinity, such as 100000000 for x, you would get a number like 3.878787878 or something similar.

 

 

 

and if you plug in a number such as 10000000000000000000000 you would get something like 3.999999999888.

 

 

 

So if you were to keep going, the number you would get would start to get closer and closer to 4, which is the answer, because although the number was not exact, it's so close that it is indistinguishable.

 

Methinks someone should understand infinity if they know math this well.

 

 

 

That's why we use fractions.

 

 

 

And no, 100000000 is not close to infinity, it was just an example to show that as the limit approaches ?, the number moves close to the answer. I literally pressed 1 and held down 0 for a second and made up an answer, I just didn't want to elongate the post any more than I had to by putting some thing like 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

 

999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

 

99999999999999999999999999999999999999999999999999999999999999999999999999.

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99999999999999999999999999999999999999999999999999999999999999999999999999 etc. is not close to infinity.

 

99999999999999999999999999999999999999999999999999999999999999999999999999^(10^74)

 

is not close to infinity.

 

(99999999999999999999999999999999999999999999999999999999999999999999999999^(10^57))^10^57

 

is not close to infinity.

 

Infinity is not really a number. it's not like once you count high enough you have reached infinity.

 

 

 

EDIT: Fixed page-stretch

 

Mod edit: Edited the numbers a little as to avoid stretching the page. ~meol

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I found this one lets see if anyone can solve it:

 

 

 

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

 

 

 

Yes. You have a 1/3 chance of getting it in the 1st place, and a 1/2 after the 1st door. However, once he asks, that changes everything (aka variable oods). If you say yes, ill change, you'll have a 66% chance of winnning.

 

 

 

Cookies to who figure outs what thats from :XD:

 

 

 

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I found this one lets see if anyone can solve it:

 

 

 

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

 

 

 

Yes. You have a 1/3 chance of getting it in the 1st place, and a 1/2 after the 1st door. However, once he asks, that changes everything (aka variable oods). If you say yes, ill change, you'll have a 66% chance of winnning.

 

 

 

Cookies to who figure outs what thats from :XD:

 

 

 

monty python of course cookies for me :thumbsup:

 

We dont have enough cookies to go around we need donations.

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[hide=]

99999999999999999999999999999999999999999999999999999999999999999999999999 etc. is not close to infinity.

 

99999999999999999999999999999999999999999999999999999999999999999999999999^(10^74)

 

is not close to infinity.

 

(99999999999999999999999999999999999999999999999999999999999999999999999999^(10^57))^10^57

 

is not close to infinity.

 

Infinity is not really a number. it's not like once you count high enough you have reached infinity.

 

 

 

EDIT: Fixed page-stretch

 

Mod edit: Edited the numbers a little as to avoid stretching the page. ~meol

[/hide]

 

 

 

infinity has properties like a number and properties unlike a number

 

 

 

my favorite example is f(x)=1/x^2

 

 

 

if x=1 then f(x)=1; if x=2 then f(x)=.5; if x=10 then f(x)=.01; if x=1000 then f(x)=.000001

 

 

 

since this pattern continues the limit as x approaches infinity f(x)=0

 

 

 

therefore f(infinity)=1/(infinity)^2=0

 

 

 

we cant reach the number infinity, but if you were to graph 1/x^2 at increasingly large numbers you would eventually get so close to 0 you would be there. The same principle that if you get half way to a wall, you will eventually be immeasurably close to the wall and we have to say you have reached it.

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Fun fact about that quote. The Chinese translation of "paradox" is actually an ancient reference to it. There's an infinitely powerful sword that will penetrate anything, and an infinitely resistant shield that can defend against anything. I remember my cousin's father telling me the story. :)

 

 

WOAH WE READ THAT STORY IN CHINESE SCHOOL

 

Or at least almost the same thing. Our version: So there's this merchant on the street, and he sells spears and shields. He says his spears can penetrate any shield, and his shields can withstand any spear. So some random dude asks what happens if you use his spear to attack his shield.

 

It never says what happens. Aw.

 

(There's a Chinese idiom about it, I'd post it if I actually remembered what it was)

 

Anyway.

 

 

2a^2=a^2+ab (what the hell did you do here? You timesd the left side of the equation by a^2 and you added a^2 to the right hand side. You fail. It should be 2a^2=ba^3)

 

You add a^2 to both sides...

 

a^2+a^2 = 2a^2

 

ab+a^2 = a^2 + ab

 

But it's not like the proof is supposed to be true.

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Doom yours still stretches page?

 

I have a pretty big screen, so it wasn't stretched on mine. I forgot that it's different on different monitors.

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Dont open hide box

 

 

 

[hide=]wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>wtf>[/hide]

 

 

 

Too many people doing that on youtube.

 

 

 

Also if the spear thing hit the shield thing the spear would lose. (Shields have a longer warrenty)

image.pl?URL=171577-4798

 

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