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Ponder This

January 2006

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Ponder This Challenge:

Puzzle for January 2006.

Consider a loop of string of unit length. Suppose we cut the string independently and at random in n places. This will divide the loop into n pieces.

This month's puzzle asks
1. What is the expected (average) size of the smallest piece?
2. What is the expected (average) size of the largest piece?

If you can't find an exact answer the asymptotic behavior (to leading order) as n goes to infinity will suffice. Please give some sort of argument to justify your answer although we will not require it to be completely rigorous.

The first 100 people who answer correctly will be listed. The answer will be posted a week after the 100th is received, or at the end of the month.

We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

We invite visitors to our website to submit an elegant solution. Send your submission to the

If you have any problems you think we might enjoy, please send them in. All replies should be sent to:


Challenge: 01/03/2006 @ 09:00 AM EST
Solution: 02/01/2006 @ 09:00 AM EST
List Updated: 02/01/2006 @ 09:00 AM EST

People who answered correctly:

Frank Yang (01.03.2006 @03:44:47 PM EDT)
Roberto Tauraso (01.04.2006 @05:38:10 PM EDT)
Balakrishnan V (01.04.2006 @05:49:07 PM EDT)
Evgeny (01.05.2006 @12:58:30 AM EDT)
Michael Swart (01.05.2006 @09:32:48 AM EDT)
Al Zimmermann (01.05.2006 @11:54:58 AM EDT)
Kennedy (01.05.2006 @03:16:10 PM EDT)
Eugene Vasilchenko (01.05.2006 @04:15:55 PM EDT)
Dan Dima (01.05.2006 @09:33:58 PM EDT)
David McKee (01.05.2006 @11:42:02 PM EDT)
Bill Schwennicke (01.06.2006 @04:16:45 PM EDT)
Huicheng Guo (01.07.2006 @12:07:33 AM EDT)
John Tromp (01.08.2006 @08:40:38 AM EDT)
Jiefeng Liang (01.08.2006 @09:53:40 PM EDT)
David McQuillan (01.09.2006 @07:04:29 AM EDT)
Katzir Liran (01.09.2006 @06:10:03 PM EDT)
Daniel Bitin (01.11.2006 @03:15:56 PM EDT)
Robert Benea (01.12.2006 @04:04:55 AM EDT)
Jian Li (01.12.2006 @06:59:39 AM EDT)
Phil Muhm (01.13.2006 @10:25:56 AM EDT)
Mike Kennedy (01.13.2006 @10:47:41 AM EDT)
Adel El-Atawy (01.14.2006 @06:32:03 AM EDT)
Yunpeng Zhou (01.14.2006 @06:08:39 PM EDT)
John G. Fletcher (01.16.2006 @05:46:48 PM EDT)
Rayadurgam Srikant (01.23.2006 @09:13:00 PM EDT)
Dharmadeep Muppalla (01.29.2006 @01:19:35 AM EDT)
Florbela I. C. G. Duarte (01.29.2006 @09:14:20 AM EDT)
Aditya Prasad (01.31.2006 @04:52:58 PM EDT)
Chris Messer (01.31.2006 @10:53:22 PM EDT)

Attention: If your name is posted here and you wish it removed please send email to the