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

Home > Probability
Creeping Ants (Posted on 2012-11-21) Difficulty: 4 of 5
At a certain time, 101 ants are placed on a one-meter stick, with one of them, Alice, placed at the exact center. The positions of the other 100 ants are random, as are the directions they face. All ants start crawling in whatever direction they are facing, always traveling at one meter per minute. When an ant meets another ant or reaches the end of the stick, it immediately turns around and continues going in the other direction. What is the probability that after 1 minute Alice is at the exact center of the stick?

No Solution Yet Submitted by Danish Ahmed Khan    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Continuing Charlie's analysis Comment 3 of 3 |

 Extending Charlie's brilliant approach, it is easily shown that after 2 minutes all ants will have reached their initial position !!!

 I find this a very surprising fact, considering that this holds for any initial distribution of the ants along the stick . 


  Posted by Dan Rosen on 2013-05-12 16:40:37
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 (9)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information