All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
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)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Computer simulation | Comment 10 of 42 |
(In reply to re: Computer simulation by Bob)

The expected value for three birds comes out in the simulation to be 3.11806 with std err 0.00804 over 100,000 trials.  You may be counting a segment or two twice to get 5 meters.

 


  Posted by Charlie on 2004-06-07 15:22:14
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (14)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information