IBM Research | Ponder This | October 2012 challenges

# Ponder This

## October 2012

<<September October November>>

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 ponder@il.ibm.com.

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

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 Jørgensen (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)
Øyvind 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)

Attention: If your name is posted here and you wish it removed please send email to the ponder@il.ibm.com.