IBM Research | Ponder This | June 2009 challenges
Skip to main content

Ponder This

June 2009

<<May June July>>


Ponder This Challenge:

Let π be a permutation on 14 elements. Define Ni as the minimal number of times the permutation π should be applied to get i back into its original place. What is the remainder, modulo 1299, of the sum over all possible 14! permutations of 4 to the power of the product of (2+the parity of Ni)? I.e, what is

As we will show in the solution, it can be computed almost on the back an envelope.

Update (06/01): Note that a fixed point (i -=> i) is considered odd (Ni=1, parity=1), and a transposition (i -=> j -=> i) is considered even (Ni=2, parity=0).


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: webmster@us.ibm.com

  

Challenge: 05/29/2009 @ 17:00 PM EST
Solution: 07/01/2009 @ 17:00 PM EST
List Updated: 07/10/2009 @ 15:00 AM EST

People who answered correctly:

Balakrishnan V. (05/29/2009 11:51 PM EDT)
John T. Robinson (05/30/2009 05:12 PM EDT)
Martin Thiim (05/31/2009 01:08 PM EDT)
Hongcheng Zhu (06/01/2009 05:31 AM EDT)
Daniel Chong Jyh Tar (06/01/2009 07:46 AM EDT)
Vladimir Sedach (06/01/2009 08:53 AM EDT)
Ionel Santa (06/01/2009 09:08 AM EDT)
Christian Blatter (06/01/2009 09:41 AM EDT)
Austin Shapiro (06/01/2009 02:14 PM EDT)
Dan Dima (06/01/2009 04:30 PM EDT)
Liubing Yu (06/01/2009 11:30 PM EDT)
Sevag Papazian (06/02/2009 09:14 AM EDT)
Michael Brand (06/02/2009 09:19 AM EDT)
Nick Miller (06/02/2009 03:42 PM EDT)
Amos Guler
(06/02/2009 05:18 PM EDT)
Pataki Gergely (06/02/2009 07:56 PM EDT)
Joe DeVincentis (06/02/2009 08:52 PM EDT)
Jochen Hoenicke (06/03/2009 10:20 AM EDT)
Corey Cerovsek
(06/03/2009 05:35 PM EDT)
Albert Stadler (06/04/2009 08:57 AM EDT)
Yu Zhangqiu
(06/04/2009 12:12 PM EDT)
Phil Muhm
(06/04/2009 02:25 PM EDT)
Rickard Bj÷rklund (06/04/2009 10:49 PM EDT)
Eli Biham (06/05/2009 11:35 AM EDT)
Andrew McFarland (06/06/2009 08:55 PM EDT)
Alan Murray (06/08/2009 12:12 PM EDT)
Clive Tong
(06/09/2009 12:44 PM EDT)
Jeff Steele (06/09/2009 09:06 PM EDT)
Nicolas Laurent (06/10/2009 05:59 AM EDT)
Ravi Shankar Ojha (06/10/2009 12:26 PM EDT)
Adam Daire (06/10/2009 02:26 PM EDT)
Daniel Bitin (06/11/2009 11:27 AM EDT)
Edgardo Deza
(06/14/2009 12:34 PM EDT)
Karthik Tadinada (06/15/2009 12:50 PM EDT)
Karl D'Souza (06/15/2009 04:49 PM EDT)
John G. Fletcher (06/15/2009 10:14 PM EDT)
Siva Dirisala
(06/17/2009 11:56 AM EDT)
Nyles Heise (06/18/2009 10:41 PM EDT)
Boris Nikolaus (06/19/2009 01:53 PM EDT)
Renato Fonseca (06/20/2009 02:58 PM EDT)
Fabio Filatrella (06/21/2009 01:00 PM EDT)
Adriana Clerici
(06/23/2009 11:49 AM EDT)
Bojan Basic
(06/24/2009 11:33 PM EDT)
Thomas Rohr
(06/25/2009 11:19 AM EDT)
John Ritson
(06/26/2009 07:55 AM EDT)
Jason L.
(06/29/2009 10:22:20 AM EDT)
Larry Rolen (06/30/2009 12:25 PM EDT)
Alex Furger
(07/01/2009 03:49 AM EDT)


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