September 2006
Puzzle for September 2006.
Let f(n) be a function on the non-negative integers defined recursively as follows:
f(0)=1, f(n)=(1+(n*n-n)*f(n-1))/(n*n+1) for n > 0. So f(1)=1/2, f(2)=2/5 ...
This month's puzzle asks for you to determine the asymptotic behavior of f(n) as n -> infinity. In other words find a simple function g(x) such that f(n)/g(n) -> 1 as n -> infinity.
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 webmaster.
If you have any problems you think we might enjoy, please send them in. All replies should be sent to: webmaster@watson.ibm.com
Challenge:
09/07/2006 @ 10:30 AM EST
Solution:
10/02/2006 @ 10:00 AM EST
List Updated:
10/02/2006 @ 11:00 AM EST
People who answered correctly:
V. Balakrishnan (09.07.2006 @11:58:45 AM EDT)
Richard Mann (09.07.2006 @04:38:17 PM EDT)
Arthur Breitman (09.07.2006 @05:15:15 PM EDT)
Dan Dima (09.07.2006 @07:57:03 PM EDT)
Oleg Trott (09.08.2006 @01:08:46 AM EDT)
Michael Quist (09.08.2006 @01:12:09 AM EDT)
Aravind (09.08.2006 @04:33:53 AM EDT)
Frank Yang (09.08.2006 @10:42:16 AM EDT)
Dinesh Krithivasan (09.08.2006 @03:04:21 PM EDT)
David McQuillan (09.08.2006 @04:32:33 PM EDT)
Lizhao Zhang (09.08.2006 @09:04:46 PM EDT)
Alan Murray (09.09.2006 @01:12:40 AM EDT)
Wolf Mosle (09.09.2006 @01:58:56 PM EDT)
Jerold Lewandowski (09.09.2006 @05:55:42 PM EDT)
Didier Bizzarri (09.09.2006 @09:05:37 PM EDT)
Arjun Acharya (09.10.2006 @02:08:20 PM EDT)
Zhou Guang (09.10.2006 @10:52:47 PM EDT)
Vincent Vermaut (09.11.2006 @10:40:49 AM EDT)
Arvind L. (09.11.2006 @11:32:28 AM EDT)
Victor Popov (09.11.2006 @05:23:35 PM EDT)
S. Amghibech (09.11.2006 @08:15:17 PM EDT)
John Fletcher (09.12.2006 @01:25:22 PM EDT)
Paolo Massaro (09.12.2006 @03:47:42 PM EDT)
Emilio Schiavi (09.12.2006 @05:37:41 PM EDT)
John T. Robinson (09.12.2006 @07:10:07 PM EDT)
John Ritson (09.13.2006 @04:05:06 AM EDT)
Piotr Zielinski (09.13.2006 @05:27:54 PM EDT)
John Dalbec (09.13.2006 @07:50:17 PM EDT)
Wu Hao (09.13.2006 @09:34:43 PM EDT)
Luke Pebody (09.14.2006 @05:43:02 AM EDT)
Matthew Samuel (09.14.2006 @11:45:19 PM EDT)
Ariel Flat (09.14.2006 @05:40:52 PM EDT)
Lawrence Hon (09.15.2006 @06:13:17 AM EDT)
Phil Muhm (09.15.2006 @10:15:57 AM EDT)
Du Yang (09.17.2006 @02:55:50 AM EDT)
Se Kwon Kim (09.18.2006 @03:13:23 AM EDT)
Mingrui Wu (09.18.2006 @08:11:28 AM EDT)
Steven Noble (09.18.2006 @11:56:28 PM EDT)
Christian Blatter (09.19.2006 @06:23:03 AM EDT)
Dion Harmon (09.19.2006 @06:11:14 PM EDT)
Dave Parashar (09.20.2006 @09:39:11 AM EDT)
Yoav Raz (09.21.2006 @12:01:06 AM EDT)
Chris Shannon (09.22.2006 @12:02:17 AM EDT)
Joachim Ripken (09.22.2006 @07:46:46 AM EDT)
Oded Margalit (09.23.2006 @04:43:19 PM EDT)
Anatoly Morosov (09.26.2006 @11:28:21 AM EDT)
Ray Gregory (09.28.2006 @10:06:13 PM EDT)
Firat Solgun (09.29.2006 @05:23:02 PM EDT)
William Hasenplaugh (09.29.2006 @07:20:25 PM EDT)
Li Han (10.01.2006 @11:39:40 AM EDT)
Attention: If your name is posted here and you wish it removed please send email to the webmaster.