IBM Research | Ponder This | October 2007 challenges

# Ponder This

## October 2007

<<September October November>>

Ponder This Challenge:

There are 5 platonic solids, the tetrahedron (4 vertices, 4 triangular faces, 6 edges), the cube (8 vertices, 6 square faces, 12 edges), the octahedron (6 vertices, 8 triangular faces, 12 edges), the dodecahedron (20 vertices, 12 pentagonal faces, 30 edges) and the icosahedron (12 vertices, 20 triangular faces, 30 edges). Consider open models of these solids with wire edges connecting the vertices. Suppose each wire has unit resistance. For each case find the total resistance between a pair of adjacent vertices. Express each answer as a rational number.

Hint: The answers can be found by brute force but there is a way to use symmetry.

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: 10/03/2007 @ 11:30 AM EDT
Solution: 11/01/2007 @ 12:00 PM EDT
List Updated: 11/02/2007 @ 04:00 PM EDT

Ashish Srivastava (10.03.2007 @12:37:09 PM EDT)
V Balakrishnan (10.03.2007 @02:44:54 PM EDT)
Chris Hills (10.03.2007 @04:05:57 PM EDT)
Dan Dima (10.03.2007 @04:21:50 PM EDT)
Jiri Navratil (10.03.2007 @07:13:21 PM EDT)
Henry Bottomley (10.03.2007 @08:39:27 PM EDT)
Celia Anteneodo (10.03.2007 @09:57:51 PM EDT)
John T. Robinson (10.03.2007 @10:52:27 PM EDT)
Gary M. Gerken (10.03.2007 @11:40:29 PM EDT)
Abhisek Ukil (10.04.2007 @05:16:10 AM EDT)
Christian Blatter (10.04.2007 @09:04:17 AM EDT)
Eugene Vasilchenko (10.04.2007 @10:44:32 AM EDT)
Frank Yang (10.04.2007 @11:57:10 AM EDT)
Karl D'Souza (10.04.2007 @08:13:19 PM EDT)
Parashar Dave (10.05.2007 @08:53:50 AM EDT)
Andreas Eisele (10.05.2007 @11:55:41 AM EDT)
Sergio Daher (10.05.2007 @02:53:32 PM EDT)
Joe Schauder (10.05.2007 @04:17:54 PM EDT)
Al Zimmermann (10.05.2007 @04:39:10 PM EDT)
Zhou Guang (10.06.2007 @10:31:56 AM EDT)
Almudena Moratinos (10.06.2007 @09:38:21 PM EDT)
Daniel Hsu (10.07.2007 @05:05:04 AM EDT)
Dion Harmon (10.07.2007 @09:27:16 PM EDT)
Renato Fonseca (10.07.2007 @10:10:09 PM EDT)
Arthur Breitman (10.08.2007 @12:30:37 PM EDT)
Fred Batty (10.08.2007 @05:52:17 PM EDT)
Alan Murray (10.08.2007 @06:09:31 PM EDT)
Jose H. Nieto (10.08.2007 @07:42:39 PM EDT)
Øyvind Grotmol (10.08.2007 @07:55:48 PM EDT)
Luke Pebody (10.08.2007 @10:22:36 PM EDT)
Ed Sheppard (10.09.2007 @12:26:15 AM EDT)
D Li (10.09.2007 @01:18:02 AM EDT)
Anneke Van Steirteghem (10.09.2007 @08:46:09 AM EDT)
Mohammed Agamy (10.09.2007 @08:51:44 PM EDT)
John Fletcher (10.10.2007 @12:22:51 AM EDT)
Victor Chang (10.10.2007 @01:26:16 AM EDT)
Michael Goldin (10.10.2007 @03:53:47 AM EDT)
Ariel Flat (10.10.2007 @09:54:19 AM EDT)
Slawek Pudlis (10.10.2007 @12:40:29 PM EDT)
Lukas Saul (10.11.2007 @01:53:59 PM EDT)
DJCV (10.12.2007 @09:28:40 PM EDT)
Maxim G. Smith (10.13.2007 @10:48:21 PM EDT)
Andrea Andenna (10.15.2007 @04:32:23 PM EDT)
John Ritson (10.15.2007 @05:29:01 PM EDT)
Yoav Raz (10.15.2007 @06:39:08 PM EDT)
Amos Guler (10.16.2007 @04:07:42 PM EDT)
Nyles Heise (10.17.2007 @08:12:47 PM EDT)
Igor Malashkin (10.18.2007 @04:19:37 AM EDT)
Phil Muhm (10.22.2007 @11:44:55 AM EDT)
Balazs Ugron (10.25.2007 @04:58:16 PM EDT)
David McQuillan (10.26.2007 @02:09:21 PM EDT)
Chris Shannon (10.26.2007 @05:56:23 PM EDT)
Joaquim Neves Carrapa (10.26.2007 @08:55:42 PM EDT)
Earl Gose (10.27.2007 @04:12:10 AM EDT)
Didier Bizzarri (10.27.2007 @09:36:21 PM EDT)
Robert Persch (10.28.2007 @03:19:42 PM EDT)
Keith F. Lynch (10.28.2007 @05:59:49 PM EDT)
Daniel Bitin (10.28.2007 @09:33:41 PM EDT)
Albert Stadler (10.30.2007 @02:47:44 AM EDT)
Gale Greenlee (10.30.2007 @10:27:26 AM EDT)
Urs Fässler (10.30.2007 @06:42:01 PM EDT)
Michael Praehofer (10.31.2007 @04:52:52 AM EDT)