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Knot or Not? (Posted on 2005-08-04) Difficulty: 1 of 5
I was walking along the road one day when I spied a cord of some sort lying in my path. From my vantage point, as I was approaching the cord, I could not tell if it was knotted or not.

What is the probability that the cord was knotted?

  Submitted by Erik O.    
Rating: 2.3333 (3 votes)
Solution: (Hide)
The problem lies in determining which of the lines are lying on top of each other at each intersection (1, 2, 3). Tracing the cord from end A to end B, the line we're following can be either Over or Under the line that's being intersected. The table below lists the eight possible scenerios and whether or not the cord is knotted:
   | 1   2   3 | Knot / Not
---+-----------+------------
 1 | O   O   O |       N
 2 | O   O   U |       N
 3 | O   U   O |   K
 4 | O   U   U |       N
 5 | U   O   O |       N
 6 | U   O   U |   K
 7 | U   U   O |       N
 8 | U   U   U |       N
As can be seen, there are eight possible ways the cord could be lying and in only two of the eight is the cord knotted. Therefore, the probability that the cord is a knot is 2/8 or 25%.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionPuzzle SolutionK Sengupta2023-12-20 02:09:18
SolutionSolutionDej Mar2008-10-04 09:46:01
AnswerK Sengupta2008-10-04 02:07:50
re: answerSean2005-10-26 12:29:54
Some ThoughtsanswerSean2005-10-26 12:23:29
Solutionlist the possible combinationstanx2005-10-18 16:25:18
Intuitive answerThomas Harris2005-08-27 20:37:11
knotty boykevin2005-08-09 20:08:46
SolutionJust right to be knottedRupesh Khandelwal2005-08-05 10:32:14
A knot not neat need not be knottedCharley2005-08-05 02:51:15
re(3): As I figure it - Definition of a knotBrian Smith2005-08-05 01:27:02
re(3): As I figure itBob Smith2005-08-04 13:49:54
ansGururaj2005-08-04 07:10:55
re(2): As I figure itRichard2005-08-04 05:28:39
re: As I figure itPaul2005-08-04 02:28:04
... O_OKristina2005-08-04 02:21:27
SolutionAs I figure itBob Smith2005-08-04 02:15:46
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