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Ponder This

October 2012

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Ponder This Challenge:

There are seven polyhedral dice in a Dungeons & Dragons game. The result of throwing the 7 D&D dice is the sum of the seven numbers from each die:

1. Tetrahedron: numbers 1, 2, 3, 4
2. Cube: numbers 1, 2, 3, 4, 5, 6
3. Octahedron: numbers 1, 2, 3, 4, 5, 6, 7, 8
4, 5. Two pentagonal trapezohedron: numbers 0,1, 2, 3, 4, 5, 6, 7, 8, 9
6. Dodecahedron: numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
7. Icosahedron: numbers 1, 2, 3, ..., 20.

Find a way to get the same distribution (same probability for each result) of tossing all seven D&D cubes by tossing four Disdyakis Triacontahedrons with integer numbers between 1 and 17 on their 120 faces.

Please supply your answer as four lines of 17 numbers. Line i describes the i-th Disdyakis Triacontahedron and Column j describes how many times the number j appears on it.


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: 09/28/2012 @ 01:00 PM EST
Solution: 11/01/2012 @ 01:00 PM EST
List Updated: 09/28/2012 @ 01:00 PM EST

People who answered correctly:

János Kramár (09/28/2012 02:52 PM EDT)
Fletcher Dostie (09/28/2012 06:33 PM EDT)
Deron Stewart (09/28/2012 07:52 PM EDT)
Anders Kaseorg (09/29/2012 02:06 AM EDT)
Radu-Alexandru Todor (09/29/2012 05:33 AM EDT)
Shilei Zang (09/29/2012 06:09 AM EDT)
Janos Csorba (09/29/2012 12:13 PM EDT)
Peter de Rivaz (09/29/2012 02:55 PM EDT)
Denys Kopiychenko (09/30/2012 12:45 PM EDT)
Mark Pervovskiy (09/30/2012 02:47 PM EDT)
Jan Fricke (09/30/2012 05:57 PM EDT)
Jochen Voß (10/01/2012 06:31 AM EDT)
Dan Dima (10/01/2012 10:46 AM EDT)
Tulasi Ram Reddy (10/01/2012 01:06 PM EDT)
Albert Stadler (10/02/2012 11:48 AM EDT)
Rino Raj (10/02/2012 12:10 PM EDT)
Lorenzo Gianferrari Pini (10/02/2012 03:09 PM EDT)
Manas Joglekar & Santosh Ananthakrishnan (10/02/2012 05:44 PM EDT)
David Friedman (10/02/2012 11:56 PM EDT)
Rob Pratt (10/03/2012 09:48 AM EDT)
Arthur Breitman (10/03/2012 03:55 PM EDT)
Michael Brand (10/03/2012 07:41 PM EDT)
Alan Murray (10/03/2012 08:55 PM EDT)
Todd Will (10/04/2012 04:15 PM EDT)
Peter Gerritson (10/04/2012 04:57 PM EDT)
Matthew Charlap (10/04/2012 06:49 PM EDT)
Joseph DeVincentis (10/05/2012 12:08 PM EDT)
Greg McNulty (10/05/2012 01:10 PM EDT)
Masoud Alipour (10/06/2012 01:38 AM EDT)
Kevin Sham (10/06/2012 03:35 AM EDT)
Daniel Kneezel (10/06/2012 04:47 AM EDT)
Adrian Orzepowski (10/06/2012 11:49 AM EDT)
Chuck Carroll (10/06/2012 01:32 PM EDT)
Balakrishnan Varadarajan (10/06/2012 08:35 PM EDT)
Guangda Huz! hang (10/06/2012 11:55 PM EDT)
Don Reble (10/07/2012 04:02 AM EDT)
Tomek Czajka (10/07/2012 08:17 PM EDT)
Xianchao Xie (10/07/2012 08:45 PM EDT)
Nis Jřrgensen (10/07/2012 10:08 PM EDT)
Dan Arnon (10/08/2012 09:01 PM EDT)
Roberto Tauraso (10/09/2012 03:16 AM EDT)
Řyvind Grotmol (10/09/2012 08:14 AM EDT)
Prateek Bhakta (10/09/2012 11:37 AM EDT)
Gautam Kamath (10/09/2012 02:43 PM EDT)
Mark Mammel
(10/09/2012 05:51 PM EDT)
Rastko Anicic (10/09/2012 06:37 PM EDT)
Kan Huang (10/10/2012 09:37 AM EDT)
Armin Krauss (10/10/2012 01:00 PM EDT)
Rogerio Ponce da Silva (10/10/2012 11:43 PM EDT)
Ken Bateman (10/11/2012 05:00 PM EDT)
Lewei Weng (10/11/2012 10:51 PM EDT)
Scott Bridges & Arthur Krebsbach (10/12/2012 02:43 PM EDT)
Eric Harley (10/14/2012 12:38 AM EDT)
Seung Min "Brian" Park (10/14/2012 10:18 AM EDT)
Alex Jeon (10/14/2012 03:52 PM EDT)
Javier Rodriguez (10/14/2012 05:12 PM EDT)
Daniel Bitin (10/14/2012 06:20 PM EDT)
Tony Harrison (10/14/2012 06:19 PM EDT)
Roddy Kok (10/15/2012 01:30 PM EDT)
Yasodhar Patnaik (10/15/2012 02:22 PM EDT)
Stéphane Higueret (10/16/2012 07:50 AM EDT)
David Greer (10/16/2012 08:10 AM EDT)
Andreas Stiller (10/16/2012 09:19 AM EDT)
Dan Ismailescu (10/16/2012 10:58 AM EDT)
Minxi Jiang (10/16/2012 12:25 PM EDT)
Siva Dirisala (10/17/2012 02:22 AM EDT)
Harald Bögeholz (10/17/2012 06:43 PM EDT)
Kevin Bauer (10/17/2012 09:47 PM EDT)
Christian Pape (10/17/2012 10:27 PM EDT)
Marcello Herreshoff (10/17/2012 11:14 PM EDT)
Oleksandr Pavlyk (10/18/2012 12:49 AM EDT)
Boris Nikolaus (10/18/2012 07:50 PM EDT)
Kartikeya Shandilya (10/19/2012 07:41 AM EDT)
Peter Holdsworth (10/19/2012 05:32 PM EDT)
Walter Schmidt (10/20/2012 06:36 AM EDT)
Gyorgy Gyomai (10/23/2012 08:05 AM EDT)
Donald Dodson (10/23/2012 06:44 PM EDT)
John Snyder (10/24/2012 02:00 PM EDT)
Alex Stangl (10/26/2012 08:49 PM EDT)
Seongwoo Hong (10/27/2012 09:50 PM EDT)
Kevin Li (10/29/2012 07:05 PM EDT)
Anunay Kulshrestha (10/30/2012 04:45 AM EDT)
Hugo Pfoertner (10/31/2012 01:24 AM EDT)
Daniel Lincke (10/31/2012 08:09 AM EDT)
Sergey Grishaev (10/31/2012 09:56 AM EDT)
Jong Wook Kim (10/31/2012 03:43 PM EDT)


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