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The Swimming Girl

08/27/2012 10:59 PM

Can we solve this problem?

In an exactly circular and very deep lake, is swimming a girl. When she is right in the center notes the proximity of a man, very strong and intelligent, but also very ugly and with evident malice, fortunately he can not swim but is able to run four times faster than she can swim, but not run as fast as she is in solid ground.

Can the girl saved from evil persecutor?

What should do the the girl to escape?

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#1

Re: The Swimming Girl

08/27/2012 11:13 PM

"What should do the the girl to escape?"

Go to another forum?

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#4
In reply to #1

Re: The Swimming Girl

08/27/2012 11:57 PM

Lol. Tnx, I needed that! :-))

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#2

Re: The Swimming Girl

08/27/2012 11:29 PM

How ugly?

How intelligent (what IQ)?

Can the girl saved from evil persecutor?

Have you heard of "circle theorem"?

What should do the the girl to escape?

A quick internet search for circle theorem, or a call to the poilce.

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#3

Re: The Swimming Girl

08/27/2012 11:53 PM

Nothing here says she has to swim in a straight line, and so this problem has an infinite number of ways she can escape - and get caught - ie, the problem is incompletely specified.

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#5

Re: The Swimming Girl

08/28/2012 12:07 AM

Well if it was that girl that sniffed the pool shock, she won't be swimming very far.

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#6
In reply to #5

Re: The Swimming Girl

08/28/2012 12:11 AM

And what about that statistician wot drowned in a lake whose average depth was 1 cm? [nuk nuk]

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#8
In reply to #5

Re: The Swimming Girl

08/28/2012 12:46 AM

Nuk nuk.

Agent Smith: It seems that you've been living two lives. One life, you're Anonymous Poster #1, poster on this thread. You have a social security number, pay your taxes, and you... help your landlady carry out her garbage. The other life is lived in computers, where you also go by the same poster alias, "Anonymous Poster #1" and are guilty of virtually every innuendo regarding Submersible Klorinated Inhalers we have a law for. One of these lives has a future, and one of them is funny as hell and has a future too. GA

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#7

Re: The Swimming Girl

08/28/2012 12:15 AM

If it was Lake Gershgorin* the girl got away and is now blogging about how the ugly brute is still there puzzling over those damned corners.

-----

(* oblique reference to an obscure theorem relating to square matrices)

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#9

Re: The Swimming Girl

08/28/2012 12:47 AM

She can swim to stay "opposite" of him as long as possible, then straight to shore, and then run.

If there are two girls, maybe they can do a Buridan's Ass strategy on him, running him ragged.

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#10
In reply to #9

Re: The Swimming Girl

08/28/2012 1:24 AM

So much for 'intelligent targeted advertising,' neh?

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#11

Re: The Swimming Girl

08/28/2012 1:51 AM

thank you and nice post...

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#15
In reply to #11

Re: The Swimming Girl

08/28/2012 7:37 AM

Thanks, it is just to have fun, and i´m getting more than imagine with all the comments, please keep your mood, and try to save the girl.

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#12

Re: The Swimming Girl

08/28/2012 4:05 AM

In the UK, ugliness is the reciprocal of beauty, which is measured in Helens (H). 1H is the beauty needed to lauch a thousand ships. It is a very large unit and is usually meaured in millihelen, the beauty needed to launch a small riverboat into an inland waterway, and the microhelen, which is the beauty needed to launch a small paper boat into a puddle.

Its reciprocal unit, H-1, is called the Nellie, which is the ugliness needed to sink a thousand ships.

Please estimate the ugliness of the man on this scale of measure, and re-post.

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#13
In reply to #12

Re: The Swimming Girl

08/28/2012 5:15 AM

SI or Imperial units? lol

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#14
In reply to #13

Re: The Swimming Girl

08/28/2012 7:34 AM

With prefixes like that, SI of course!

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#16
In reply to #14

Re: The Swimming Girl

08/28/2012 7:40 AM

Nothing like brevity, especially when you don't try to speak what SI stands for lol

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#17
In reply to #12

Re: The Swimming Girl

08/28/2012 7:49 AM

I think that for the girl you can take 500 millihelen and for the man 500 millinellie, sound good enougth to me to use your old english units. Thanks

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#19
In reply to #17

Re: The Swimming Girl

08/28/2012 9:45 AM

Millihelen? I am unfamiliar with that. How many millihelen are in one henway?

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#22
In reply to #19

Re: The Swimming Girl

08/28/2012 10:27 AM

Please reffer to the #12 comment, just is a joke

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#23
In reply to #22

Re: The Swimming Girl

08/28/2012 10:33 AM

As is the henway, my friend! It's just a joke... we'll see if someone obliges us with the proper setup for the joke to become evident.

At least I did not ask you about a duckdo.

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#24
In reply to #23

Re: The Swimming Girl

08/28/2012 12:55 PM

OK, in reference to #19, what's a henweigh?

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#26
In reply to #24

Re: The Swimming Girl

08/28/2012 1:22 PM

"...what's a henweigh?"

Oh, about three pounds.

Thanks to lyn for playing the straight man!

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#27
In reply to #26

Re: The Swimming Girl

08/28/2012 2:03 PM

Would those be pounds sterling or pounds sand up the arse?

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#29
In reply to #23

Re: The Swimming Girl

08/28/2012 2:30 PM

Just to keep it warm, I can guess a Henway is a meassure of the number of steps should do a hen to her nest after a fifth type contact with her cock.

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#30
In reply to #29

Re: The Swimming Girl

08/28/2012 2:33 PM

Just goes to show you that any cock'll do. I mean cock a doodle do. I mean ... never mind.

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#33
In reply to #30

Re: The Swimming Girl

08/28/2012 2:38 PM

Now we can change the problem to a "swimming hen" and an "ugly cock"

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#34
In reply to #33

Re: The Swimming Girl

08/28/2012 2:48 PM

I can honestly say, I didn't see this coming!

Language irregularities can be quite interesting, that's for sure!

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#35
In reply to #34

Re: The Swimming Girl

08/28/2012 2:50 PM

[animated GIF envy]

You were saying?...

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#40
In reply to #33

Re: The Swimming Girl

08/31/2012 5:03 AM

Ye gods...

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#41
In reply to #40

Re: The Swimming Girl

08/31/2012 2:11 PM

From what I can see, everyone was being silly (including me), 40 funny comments, but last night I wake up at 3 in the morning with the solution in my mind, the interesting thing is how the brain is functioning: the girl can reach the border 0.14R before the man. Now you can keep pulling legs.

Thanks all

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#42
In reply to #41

Re: The Swimming Girl

08/31/2012 2:56 PM

Okay, Mr. Sleepyhead, what if the bloke could run faster than the girl can swim by a factor of ∏+1?

and (be still my heart)

Need the girl's trajectory between the center and the shore be everywhere differentiable?

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#43
In reply to #42

Re: The Swimming Girl

08/31/2012 4:24 PM

Dear Europium:

Thanks for all

My first approach was to seek a differential equation, later through a computer simulation I come to the conclusion that the girl has a real chance to save herself, but I could not find an analytical solution, finally, as I said, I found an easy solution in my dreams, just keep in mind that the girl, when near the center, has an angular velocity greater than that of the man, this means that she is able to localizes herself in the best place to start swimming right to the edge, the best place is at a distance of 0.25 R from the center with the man on the opposite side, when in this position may directly swim to the edge.

Kind regards

Ciro

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#44
In reply to #43

Re: The Swimming Girl

08/31/2012 5:56 PM

Hmmm...I dreamt I won the lottery... How far is Lima by yacht? (The girl's aboard, btw. I'm the ugly brute) :-) Your solution is correct. Her trajectory is optimally a spiral until she is R/4 from the center, at which point she can swim radially straight to shore. She'll meet the ugly bloke of course, and that's when she hands me that electric eel from another post. :) The first part is easy when you solve in polar coordinates. She swims such that her angular displacement is always his a.d. plus pi radians, always keeping the circle centre directly between the bloke and herself, co-linear style. The path she traces at his rate / 4, and so her radial distance must adjust accordingly whilst the angular part varies at a constant rate, hence the progressively-flatter spiral shape. And no, the optimal trajectory is *not* everywhere differentiable. Cheers!

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#45
In reply to #43

Re: The Swimming Girl

09/02/2012 9:30 AM

My OCD kicking in again. You are very close.

Given:
R=lake radius
r=swimmer position radius (0 => r => R)
Vr=4*Vs (runner is 4x faster than swimmer)

Then:
r > (1-Pi/4)*R (swimmers time to shore is less than runner intercept time)
r > 0.2146*R

and...

r < 0.2500*R (swimmers radial velocity is greater than runner radial velocity)

The girl must swim out to a radius r (where 0.2146*R < r < 0.2500*R) and swim in a circle. Her radial velocity will be greater than her pursuer so she should be able to reach a position directly opposite his position. She can then swim directly to shore before he can intercept her. Interesting puzzle. Thanks for the distraction

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#46
In reply to #45

Re: The Swimming Girl

09/02/2012 12:54 PM

Opps x3... should be radial angular velocity.

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#47
In reply to #46

Re: The Swimming Girl

09/02/2012 1:05 PM

No donut for you!

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#48
In reply to #45

Re: The Swimming Girl

09/02/2012 1:08 PM

As Old Lead-Bottom (my 8th-grade math teacher whose formidable nether regions no doubt inspired the Hip-Hop genre) used to intone: "Show your work!"

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#49
In reply to #45

Re: The Swimming Girl

09/02/2012 1:18 PM

Close??

Been Columbus in XXI ???

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#31
In reply to #29

Re: The Swimming Girl

08/28/2012 2:33 PM
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#32
In reply to #31

Re: The Swimming Girl

08/28/2012 2:38 PM

What're you so embarrassed about? Haven't you ever lived on a farm? Cock-fights in the henways amongst the paltry poultry? I mean, GOSH!

Here, have a pullet surprise.

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#36
In reply to #32

Re: The Swimming Girl

08/28/2012 3:30 PM

I was raised on a farm. I remember smiling when my 10 year old town cousin came to visit and exclaimed, "Oh look, that one cow is hitching a ride on the other one."

I didn't explain the facts of life to him, I thought I'd let the parents deal with that one.

"pullet surprise" That's a good one. Anybody seen the blue prince of the house?

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#20
In reply to #12

Re: The Swimming Girl

08/28/2012 9:51 AM

So that's where the phrase "Whoa, Nellie" originated?

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#25
In reply to #12

Re: The Swimming Girl

08/28/2012 1:04 PM

Now I am actually glad I read this stupid post.

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#37
In reply to #25

Re: The Swimming Girl

08/28/2012 5:39 PM

Are you quite sure? Lololol

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#18

Re: The Swimming Girl

08/28/2012 8:07 AM

Welcome, Ciro, to CR4! You're quite a rarity. How many S. American CR4 members here? Three or four out of CR4's what, 60,000 members?

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#21
In reply to #18

Re: The Swimming Girl

08/28/2012 10:24 AM

Thanks to you Europio, I think the languages difficulties is the main reason for the the small participation of S Americans. To write a few words i take probably much more time than you do, but it is nice to be in contact with the CR4 people and i can practice my english too.

Reggards

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#28
In reply to #21

Re: The Swimming Girl

08/28/2012 2:04 PM

Well, your English is a lot better than my Lima, Peruvian and my English put together! lol

Uh oh, I think the dunny's leaking again....

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#38

Re: The Swimming Girl

08/28/2012 10:06 PM

She should grab an electric eel and use it to intimidate her antagonist.....

Honey you didn't just catch him dinner...be menacing! Casting we might need a scarier mermaid....

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#39
In reply to #38

Re: The Swimming Girl

08/28/2012 10:41 PM

Marital aid?

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