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Bird on a Wire (Posted on 2004-06-07) Difficulty: 5 of 5
A telephone wire stretched tight between two poles placed ten meters apart is a favorite resting spot for a flock of crows.

Suppose one morning two crows land on the wire, each at a random spot (the probability is uniformly distributed). With a bucket of paint and a brush you mark the stretch of wire between them. A certain length of wire will have been painted.

On average, what length of wire would you expect to have painted? Assume that each bird is a single point along the line, and so has no width.

Suppose instead that a dozen crows landed on the wire, each at an independent, random location, and you painted the stretch of wire between each bird and its nearest neighbor. On average, what total length of wire would you expect to have painted now?

And if a thousand crows landed?

A computer-generated solution could be found, but bonus points will be awarded for a formal proof!

No Solution Yet Submitted by Sam    
Rating: 3.7000 (10 votes)

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  Subject Author Date
Hints/TipsN Bird Case (1)FrankM2008-02-03 22:01:06
Solution2 birds, 1 stoneFrankM2008-02-03 12:14:38
SolutionStrange, I get 2ln1,5 - 3/8 ~ .43593FrankM2008-01-18 00:14:53
I might have the solution if i got the question right :DEthen Hunt2004-09-09 09:17:12
re(6): Full solutionBon2004-08-05 16:12:26
re(5): Full solutionCharlie2004-08-04 21:59:52
re(4): Full solutionBon2004-08-04 17:44:30
re(3): Full solutionThoughtProvoker2004-07-30 06:22:34
re(2): Full solutionBon2004-07-30 04:49:07
re: Full solutionCharlie2004-07-13 08:19:47
SolutionFull solutionBon2004-07-12 17:52:56
solution?Aaron2004-07-01 21:16:35
answerRob2004-06-13 01:05:30
re: What the problem is askingRichard2004-06-09 13:28:07
re(4): Concrete Answer is (n-1)/(n+1)Richard2004-06-09 13:17:58
re(3): Concrete Answer is (n-1)/(n+1)Charlie2004-06-09 11:16:34
What the problem is askingJer2004-06-09 09:17:35
Some ResearchRichard2004-06-09 00:13:58
re(2): Concrete Answer is (n-1)/(n+1)Richard2004-06-08 21:23:16
re: Concrete Answer is (n-1)/(n+1)Charlie2004-06-08 20:26:58
Concrete Answer is (n-1)/(n+1)Richard2004-06-08 18:11:35
re(7): Computer simulation -- CORRECTION !!Erik O.2004-06-08 08:32:43
re(6): Computer simulation -- CORRECTION !!Penny2004-06-08 07:46:06
SolutionSolutionPenny2004-06-08 06:56:11
re: Abstract AnswerRichard2004-06-08 05:22:06
a guessrixar2004-06-07 22:25:45
Abstract AnswerRichard2004-06-07 20:15:36
re(5): Computer simulation -- CORRECTION !!Charlie2004-06-07 20:07:16
(probably repetitive) 2 and 3 bird solutionTristan2004-06-07 19:20:11
re(4): Computer simulationEric2004-06-07 17:23:36
SolutionAlmost completeCharlie2004-06-07 15:44:05
re(3): Computer simulationCharlie2004-06-07 15:38:41
re(2): Computer simulationCharlie2004-06-07 15:22:14
Two BirdsRichard2004-06-07 15:02:49
re: Computer simulationEric2004-06-07 14:55:47
Some Thoughtsre(2): Some thoughts on the 2 bird problem. (partial solution)Danny2004-06-07 14:49:37
Some Thoughtsre(2): Some thoughts on the 2 bird problem. (partial solution)Erik O.2004-06-07 14:42:22
re: Some thoughts on the 2 bird problem. (partial solution)Eric2004-06-07 14:04:32
Some ThoughtsComputer simulationCharlie2004-06-07 13:56:29
Some ThoughtsSome thoughts on the 2 bird problem. (partial solution)Erik O.2004-06-07 13:56:13
ThoughtsEric2004-06-07 13:38:59
QuestionClarification please?Erik O.2004-06-07 12:55:59
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