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Ponder This

November 2002

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Ponder This Challenge:

This month's puzzle comes from David Gamarnik, who heard it after a wedding in the Republic of Georgia.
You are blindfolded. In front of you is a square turntable with four bottles at the corners. Each might be oriented "up" or "down". You make a sequence of "moves". Each move consists of five phases:
(1) A referee turns the table an unknown number of quarter-turns;
(2) You select "adjacent" or "opposite", and then take a pair of bottles which are either "adjacent" (90 degrees apart) or "opposite" (180), accordingly.
(3) You observe (by touch) the current orientation of these two bottles.
(4) You turn over one or the other bottle, or neither, or both.
(5) The referee tells you whether all four bottles are in the same orientation; if so, you win and the game is over.

After how many moves can you guarantee that you will have won?
What is your strategy?

Extra credit:
Prove that this is the minimum number of moves for which a guarantee can be made.


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Challenge: 11/01/02 @ 1:00 PM EST
Solution: 11/30/02 @ 9:00 AM EST
List Updated: 11/01/02 @ 1:00 PM EST

People who answered correctly:


Vineet Gupta
(11.01.2002@02:07:36PM EST)

Louis Slothouber (11.01.2002@04:04:37PM EST)
Stephen Martin (11.01.2002@05:27:10PM EST)
Michael Malak (11.01.2002@05:47:38PM EST)
Vladimir Sedach (11.01.2002@05:59:14PM EST)
Ross Millikan (11.01.2002@06:06:20PM EST)
Sriraman M Tallam (11.01.2002@06:53:32PM EST)
Mohan Rajagopalan (11.01.2002@06:53:32PM EST)
Dean M Starrett (11.01.2002@08:16:27PM EST)
Joseph DeVincentis (11.01.2002@08:33:42PM EST)
Wu Zheng (11.01.2002@08:57:07PM EST)
Frank Mullin (11.01.2002@10:06:19PM EST)
Shashidhar V (11.02.2002@01:13:18AM EST)
Arun Gautam (11.02.2002@07:31:40AM EST)
Manoj Kumar (11.02.2002@09:06:19AM EST)
Jonathan Wildstrom (11.02.2002@10:31:46AM EST)
Hazem D. Elmeleegy (11.02.2002@11:32:52AM EST)
William Heller (11.02.2002@03:07:52PM EST)
Vitaly Stakhovsky (11.02.2002@08:28:51PM EST)
Chetan Kamat (11.03.2002@01:11:45AM EST)
David P Woodruff (11.03.2002@01:59:49AM EST)
G V R Anand (11.03.2002@04:23:00AM EST)
Kozma Laszlo (11.03.2002@08:13:42AM EST)
Gil Better (11.03.2002@08:16:55AM EST)
Sarang Aravamuthan (11.03.2002@10:33:48AM EST)
Michael Brand (11.03.2002@11:56:17AM EST)
Matthew Martin (11.03.2002@01:48:14PM EST)
Jeffrey Lebak (11.03.2002@01:48:14PM EST)
John Ritson (11.03.2002@06:31:47PM EST)
Vincent Lynch (11.03.2002@07:08:52PM EST)
Anthony Coore (11.03.2002@11:11:13PM EST)
Juraj Weisz (11.04.2002@03:51:57AM EST)
Dan Ungureanu (11.04.2002@03:54:58AM EST)
Jonathan Wildstrom (11.04.2002@09:44:27AM EST)
Srihari Adireddy (11.04.2002@10:23:06AM EST)
Tim Deegan (11.04.2002@11:21:29AM EST)
Peter Huggins (11.04.2002@12:06:15AM EST)
Francis Golding (11.04.2002@01:03:24PM EST)
Yuvraj Singh Dhillon (11.04.2002@01:19:20PM EST)
Karl D'Souza (11.04.2002@01:45:45PM EST)
Michael Swart (11.04.2002@04:45:10PM EST)
Philippe J Sartori (11.04.2002@04:46:51PM EST)
Christopher Howe (11.04.2002@05:19:33PM EST)
Michael P. Moyer (11.04.2002@08:37:06PM EST)
Ashish Mishra (11.04.2002@08:42:14PM EST)
Alex Wagner (11.04.2002@10:45:33PM EST)
Ravivrat Pandey (11.05.2002@02:01:00AM EST)
Gyora Benedek (11.05.2002@05:22:56AM EST)
Pedro (11.05.2002@07:46:56AM EST)
Dan Florescu (11.05.2002@08:53:18AM EST)
Cosmin Arad (11.05.2002@11:17:25PM EST)
Aleksandar Damnjanovic (11.05.2002@11:35:55AM EST)
Pascal Brisset (11.05.2002@12:59:03PM EST)
Sriram K. Rallabhandi (11.05.2002@04:45:00PM EST)
Jayavel Sounderpandian (11.05.2002@06:33:15PM EST)
Lavanya Kannan (11.05.2002@10:02:07PM EST)
Traian Dajma (11.06.2002@08:08:43AM EST)
Drahovsky Jozef (11.06.2002@08:55:42AM EST)
Alan O'Donnell (11.06.2002@11:02:53AM EST)
Dan Schwarz (11.06.2002@11:28:14AM EST)
Buckeye GSS (11.06.2002@12:23:45AM EST)
Shmuel Spiegel (11.06.2002@12:36:36AM EST)
Francois Galilee (11.06.2002@02:11:50PM EST)
Daniel A Clymer (11.06.2002@06:30:02PM EST)
Roger D Thompson (11.07.2002@05:58:54AM EST)
Peter Cervenanský (11.07.2002@08:30:52AM EST)
Tal Weiss (11.07.2002@11:52:03AM EST)
Joe Vanore (11.07.2002@02:29:52PM EST)
Kishore Gangwani (11.07.2002@05:58:18PM EST)
Sauraj Goswami (11.07.2002@06:59:36PM EST)
Ervan Darnell (11.08.2002@01:54:01AM EST)
Gaurav Bhalotia (11.08.2002@03:00:49AM EST)
Marko Vogrin (11.08.2002@02:56:45PM EST)
Ryan Mickler (11.08.2002@07:07:04AM EST)
Frans Buijsen (11.08.2002@10:07:11AM EST)
Will Jarvis (11.08.2002@11:52:00AM EST)
JP Sugarbroad (11.08.2002@03:13:42PM EST)
Ibrahim Okuyucu (11.09.2002@04:19:31AM EST)
Maxim G. Smith (11.09.2002@10:36:43AM EST)
Claudio Baiocchi (11.11.2002@04:00:02AM EST)
Rok Jamnik (11.11.2002@07:23:02AM EST)
Roger Duthie (11.11.2002@07:46:09AM EST)
Hagen von Eitzen (11.11.2002@07:59:02AM EST)
Frank (11.11.2002@10:33:06AM EST)
Suryaprasad Kareenahalli (11.11.2002@11:58:00AM EST)
Soonho you (11.11.2002@09:33:00 PM EST)
Grant Lammi (11.11.2002@11:26:07PM EST)
Chip Lynch (11.12.2002@02:08:05AM EST)
Cristian Mocanu (11.12.2002@03:33:34AM EST)
Nachiket Bapat (11.12.2002@05:06:02PM EST)
Stephen E. F. Villee (11.12.2002@10:20:15PM EST)
John G. Fletcher (11.13.2002@01:20:16AM EST)
Nick Jones (11.13.2002@12:00:46PM EST)
Narayanan Rajamani (11.13.2002@10:44:54PM EST)
Vivek Kumar Mehra (11.14.2002@07:39:38AM EST)
Mark Pilloff (11.14.2002@05:50:00PM EST)
Vivek Parashar (11.15.2002@07:37:00AM EST)
Suresh Ramakrishnan (11.15.2002@04:08:08PM EST)
Clive Tong (11.15.2002@04:15:57PM EST)
Hassan Masum (11.16.2002@10:49:45AM EST)
Daniel Wood (11.16.2002@12:01:02AM EST)
Nandakumar R. (11.17.2002@02:33:51AM EST)
Gaurav Agrawal (11.17.2002@05:26:40AM EST)
Itsik Horovitz (11.17.2002@06:52:55AM EST)
Mukul Madhukar Joshi (11.17.2002@10:36:04AM EST)
Suresh Ganesan (11.18.2002@04:54:44AM EST)
Ziga Hajdukovic (11.18.2002@06:41:05AM EST)
Colin Pinto (11.18.2002@10:33:19AM EST)
Peter Bennett (11.18.2002@10:34:00AM EST)
Daniel Bitin (11.18.2002@10:42:48AM EST)
Mrinalini T. Chaturvedi (11.18.2002@02:48:00PM EST)
Shriram Bharath (11.18.2002@06:22:00PM EST)
Mitchell A. Kaplan (11.18.2002@11:30:10PM EST)
Sameer Pawanekar (11.19.2002@07:49:00AM EST)
Stephane Higueret (11.19.2002@08:15:55AM EST)
Jan Rüten-Budde (11.19.2002@12:52:26PM EST)
Chris Shannon (11.19.2002@10:20:52PM EST)
Liu Jianjun (11.20.2002@12:33:06AM EST)
Gregory Dietrich (11.20.2002@04:26:58AM EST)
Christopher Yao (11.22.2002@06:51:22AM EST)
Andrew Rose (11.22.2002@09:57:19AM EST)
Nagendra (11.24.2002@11:49:15PM EST)
Pradeep S Bhatt (11.25.2002@08:05:40AM EST)
Mihai Cioc (11.25.2002@05:59:57PM EST)
Paul Reiners (11.26.2002@04:25:03PM EST)
Liu Wei (11.28.2002@02:55:00AM EST)
Taku Tamagawa (11.28.2002@03:38:46AM EST)
Guler Amos (11.28.2002@01:10:42PM EST)
Nikhil Sahasrabudhe (11.29.2002@02:43:11AM EST)
Biju Mohan (11.29.2002@04:15:36AM EST)
Paul Gover (11.29.2002@05:25:15AM EST)
Ebi Aharpour (11.30.2002@11:19:51AM EST)
Vaithianathan A (12.02.2002@04:23:28AM EST)



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