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#1 2013-08-09 00:24:41

anna_gg
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Shoelace

A shoelace is lying on the floor, and attached you can see its shadow. If I pull it, what is the probability that it will produce a knot?


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#2 2013-08-09 01:03:53

anonimnystefy
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Re: Shoelace

Hi anna_gg


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#3 2013-08-09 01:18:25

anna_gg
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Re: Shoelace

All I can tell is that there are 7 intersections, so there are 2^7 =128 possible ways the shoelace can cross itself. Of these, we should keep only the ones that are "over/under/over" and "under/over/under", which will produce a knot. But I cannot figure out how many these are.

 

#4 2013-08-09 01:30:46

anonimnystefy
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Re: Shoelace

Um, have you seen my answer?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#5 2013-08-09 01:46:38

anna_gg
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Re: Shoelace

anonimnystefy wrote:

Um, have you seen my answer?

Yes, but I do not understand how you calculate it smile

 

#6 2013-08-09 04:29:18

anonimnystefy
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Re: Shoelace

Well, I looked at the two parts separately, because they are virtually independent. For one, there are 8 possibilities for one and 16 for the other. Then I just combine them.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#7 2013-08-10 03:47:55

anna_gg
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Re: Shoelace

anonimnystefy wrote:

Well, I looked at the two parts separately, because they are virtually independent. For one, there are 8 possibilities for one and 16 for the other. Then I just combine them.

So you mean that in the right part there are only 3/16 possibilities that a knot is produced? Because at the left part I see there are 2/8, that is 4/16.

 

#8 2013-08-10 03:51:50

anonimnystefy
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Re: Shoelace

No, both probabilities are 1/4.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#9 2013-08-10 04:48:28

anna_gg
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Re: Shoelace

anonimnystefy wrote:

No, both probabilities are 1/4.

So, how do you get 7/16? Am confused smile

 

#10 2013-08-13 02:51:14

anna_gg
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Re: Shoelace

Got it. You don't add the two sections, you multiply them smile

 

#11 2013-08-13 02:55:28

bobbym
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Re: Shoelace

How did you get 7 / 16 by multiplying?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#12 2013-08-13 17:28:11

anna_gg
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Re: Shoelace

bobbym wrote:

How did you get 7 / 16 by multiplying?

The probability for both parts NOT to produce a knot is 3/4 for each (since the probability to produce a knot is 1/4). Therefore the total probability NOT to have a knot is 3/4*3/4 = 9/16, thus giving us probability to have a knot 1-9/16 = 7/16.

It wasn't me who solved it, I just unraveled anonimnystefy's solution smile

 

#13 2013-08-13 18:09:32

bobbym
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Re: Shoelace

Hi;

Okay, thanks for the answer.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#14 2013-08-18 23:32:09

bohr
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Re: Shoelace

I understand that the left part has a probability of 1/4 to produce a knot, since only two of the eight possible ways produce a knot (over/under/over and under/over/under). However, how the right part has also 1/4 probability; You mean that from the 16 possible ways, 4 of them produce a knot;

 

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