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Ponder This

June 2009

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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).


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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)


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