IBM Research | Ponder This | July 2014 challenges

# Ponder This

## July 2014

<<June July August>>

Ponder This Challenge:

32 pebbles are placed on the six edges of a tetrahedron, as shown in the following figure.

Two players are playing a game. Each player, on her turn, can take as many pebbles as she chooses, but a minimum of one pebble must be taken each turn, and all the pebbles taken must be on the same face. If you cannot play (i.e., if all the pebbles are taken) - you lose.

What are the winning moves, for the first player, in this situation?

For example, if the first player plays 0,0,3,0,8,13 i.e., taking the whole northeast face, leaving the tetrahedron as 1,2,0,5,0,0; then the second player can win by playing 0,1,0,4,0,0 on the bottom face which leaves 1,1,0,1,0,0; and for every possible move of the first player, the second player can immediately win.

Please supply your answer as a list of lines, each line is a possible move.

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: 07/01/2014 @ 11:00 AM EST
Solution: 08/01/2014 @ 01:00 PM EST
List Updated: 06/30/2014 @ 01:00 PM EST

### People who answered correctly:

Reiner Martin (07/01/2014 01:20 PM EDT)

Donald Dodson (07/01/2014 01:32 PM EDT)
Todd Will (07/01/2014 02:15 PM EDT)
Florian Fischer (07/01/2014 02:36 PM EDT)
Fletcher Dostie (07/01/2014 05:20 PM EDT)
Anatoli Plotnikov (07/01/2014 06:57 PM EDT)
James Dow Allen (07/01/2014 07:19 PM EDT)
Christian Häggström (07/02/2014 07:52 AM EDT)
Benjamin Phillabaum (07/02/2014 05:51 PM EDT)
Sean Egan (07/03/2014 02:32 AM EDT)
Daniel Bitin (07/03/2014 06:13 AM EDT)
Graham Hemsley (07/03/2014 05:56 AM EDT)
Adly Templeton & Duane Bailey (07/03/2014 09:51 AM EDT)
Michael Rosola (07/04/2014 08:56 AM EDT)
Philip Kinlen (07/05/2014 01:35 AM EDT)
Adrian Orzepowski (07/05/2014 03:47 AM EDT)
Chuck Carroll (07/05/2014 06:00 AM EDT)
Alexandre Gilotte (07/05/2014 02:46 PM EDT)
Olivier Mercier (07/06/2014 12:18 AM EDT)
Emilio Del Tessandoro (07/06/2014 06:11 PM EDT)
Gurvan Lullien (07/07/2014 02:54 PM EDT)
Peter Gerritson (07/07/2014 03:21 PM EDT)
Daniel Johnson (07/07/2014 08:57 PM EDT)
Shunyu Yao (07/07/2014 11:59 PM EDT)
Clive Tong (07/08/2014 02:51 AM EDT)
David Brink & Claus Andersen
(07/08/2014 08:37 AM EDT)
Andrea Andenna (07/08/2014 06:50 PM EDT)
Melvin Tsang (07/09/2014 10:23 AM EDT)
Gilles-Philippe Paillé (07/10/2014 03:21 PM EDT)
P Sajjan Raj Jain & Mahesh Dhabade & Madhusudan Aremallenahally Shivanna (07/11/2014 10:16 AM EDT)
Yue Ru Sun (07/11/2014 11:26 AM EDT)
Jan Fricke (07/12/2014 07:41 AM EDT)
Alex Fleischer (07/12/2014 08:05 AM EDT)
Motty Porat (07/12/2014 03:28 PM EDT)
David Friedman (07/13/2014 01:16 AM EDT)
William Heller (07/14/2014 11:30 AM EDT)
Yuliang Li (07/14/2014 08:04 PM EDT)
Ariel Ish-Shalom (07/14/2014 11:35 PM EDT)
Mathias Schenker (07/15/2014 03:41 AM EDT)
Hakan Summakoglu (07/15/2014 06:34 AM EDT)
Cynthia Beauchemin (07/15/2014 12:10 PM EDT)
Péter Móra (07/16/2014 01:28 AM EDT)
Liubing Yu (07/16/2014 08:29 AM EDT)
Joaquim Neves Carrapa (07/16/2014 06:23 PM EDT)
Viktor Chayko & Aliaksei Vaidzelevich (07/18/2014 05:53 AM EDT)
Kevin Bauer (07/21/2014 02:01 PM EDT)
Michel Hannoyer (07/23/2014 03:30 AM EDT)
Abhinav Kumar (07/23/2014 10:11 PM EDT)
Chris Shannon (07/25/2014 02:46 AM EDT)
Franciraldo Cavalcante (07/25/2014 09:22 PM EDT)
Nyles Heise (07/25/2014 11:12 PM EDT)
Victor Chaves (07/26/2014 07:14 PM EDT)
Langechuan Liu (07/26/2014 07:50 PM EDT)
Armin Krauss (07/28/2014 01:52 PM EDT)
Joe Klobusicky (07/28/2014 02:39 PM EDT)
David Greer (07/28/2014 06:18 PM EDT)
Oleg Vlasii (07/29/2014 04:32 PM EDT)
Sergey Koposov (07/29/2014 05:39 PM EDT)
Radu-Alexandru Todor (07/30/2014 05:29 PM EDT)
Ehud Schreiber (07/31/2014 05:42 AM EDT)

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