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        riddles >> medium >> Knot
        
(Message started by: Altamira_64 on Aug 8^th, 2013, 7:21am)

Title: Knot
Post by Altamira_64 on Aug 8^th, 2013, 7:21am

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?

Title: Re: Knot
Post by Altamira_64 on Aug 12^th, 2013, 1:19am

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?

Title: Re: Knot
Post by Grimbal on Aug 12^th, 2013, 9:28am

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.

Title: Re: Knot
Post by Altamira_64 on Aug 12^th, 2013, 9:52am

Great, thanks!!

Title: Re: Knot
Post by webtasarim on Oct 6^th, 2013, 3:56pm

nice explanation thanks