Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

## #1 2013-08-09 00:24:41

anna_gg
Full Member

Offline

### 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?

## #2 2013-08-09 01:03:53

anonimnystefy
Real Member

Offline

### 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
Full Member

Offline

### 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
Real Member

Offline

### 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
Full Member

Offline

### Re: Shoelace

#### anonimnystefy wrote:

Um, have you seen my answer?

Yes, but I do not understand how you calculate it

## #6 2013-08-09 04:29:18

anonimnystefy
Real Member

Offline

### 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
Full Member

Offline

### 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
Real Member

Offline

### 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
Full Member

Offline

### Re: Shoelace

#### anonimnystefy wrote:

No, both probabilities are 1/4.

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

## #10 2013-08-13 02:51:14

anna_gg
Full Member

Offline

### Re: Shoelace

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

## #11 2013-08-13 02:55:28

bobbym

Online

### Re: Shoelace

How did you get 7 / 16 by multiplying?

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #12 2013-08-13 17:28:11

anna_gg
Full Member

Offline

### 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

## #13 2013-08-13 18:09:32

bobbym

Online

### Re: Shoelace

Hi;

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #14 2013-08-18 23:32:09

bohr
Novice

Offline

### 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;