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

Home > Probability
Shoelaces (Posted on 2005-04-05) Difficulty: 3 of 5
You have a drawer with n shoelaces in it. You reach into the drawer and select two lace ends at random, and tie them together. Repeat this until there are no more untied lace ends left.

If the two ends are from the same lace, or from the same group of laces already tied at their ends, it will form a loop, and therefore no longer have any free ends.

Continue this until all laces are parts of loops, of either 1 lace, 2 laces, etc.

When you're finished, a certain number of loops will have been formed in this fashion, consisting of one or more laces.

What is the expected number of loops?

See The Solution Submitted by Charlie    
Rating: 3.8333 (6 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Answer Comment 7 of 7 |

The required expected number of loops is:

 1 + 3^-1 + 5^-1 + .....+ (2n-3)^-1 + (2n-1)^-1

Edited on October 5, 2008, 2:32 am
  Posted by K Sengupta on 2008-10-05 02:31:27

Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2019 by Animus Pactum Consulting. All rights reserved. Privacy Information