Author |
Topic: Knot (Read 2689 times) |
|
Altamira_64
Junior Member
Posts: 116
|
A shoelace is lying on the floor, and attached you can see its shadow. If I pull it, what’s the probability that it will produce a knot?
|
|
 IP Logged |
|
|
|
Altamira_64
Junior Member
Posts: 116
|
 |
Re: Knot
« Reply #1 on: Aug 12th, 2013, 1:19am » |
 Quote  Modify
|
All I can tell is that at the left part, there are 3 intersections and therefore 2^3=8 different ways for the shoelace to cross itself, but of those, only 2 (ud/down/up or down/up/down) will produce a knot. For the right part, I am not sure, though... 4 intersections, therefore 2^4=16 different ways, but how many of them do produce a knot?
|
|
IP Logged |
|
|
|
Grimbal
wu::riddles Moderator
Uberpuzzler
Gender: 
Posts: 7527
|
|
Re: Knot
« Reply #2 on: Aug 12th, 2013, 9:28am » |
Quote Modify
|
Since when do shoelaces make a closed loop? 
Anyway: Considering the top 2 intersections on the right side, if both are "horizontal up" or both "horizontal down" then it is a free loop that can be moved from the top strand and the rest can be untwisted if necessary.
The same applies to the two middle intersections on the right.
If none of this applies, then either way, it is a simple knot or a eight-knot. So there is 3/4 chances to be knot free on the right.
With the 3/4 chances on the left that makes 9/16 to be knot free, or a 7/16 probability to have a knot.
In real life, though, you might end up with a knot even when topology says it is impossible.
|
| « Last Edit: Aug 12th, 2013, 9:29am by Grimbal » |
IP Logged |
|
|
|
Altamira_64
Junior Member
Posts: 116
|
|
Re: Knot
« Reply #3 on: Aug 12th, 2013, 9:52am » |
Quote Modify
|
Great, thanks!!
|
|
IP Logged |
|
|
|
webtasarim
Newbie
  
Gender:
Posts: 47
|
|
Re: Knot
« Reply #4 on: Oct 6th, 2013, 3:56pm » |
Quote Modify
|
nice explanation thanks
|
|
IP Logged |
|
|
|
|
RIDDLES SITE
WRITE MATH!
Home 
Help 
Search 
Members 
Login 
Register
Reply
Notify of replies
Send Topic
Print