March 2014
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N lamps are set in a circle, and for each integer M you have a tool that can toggle the state (on/off) of any set of M consecutive lamps.
Find a possible N which satisfies the following statements:
- The sum of its digits is less than 10.
- By applying the tool for M=105 several times, we can toggle a single lamp.
- If we remove one lamp and start from a random initial setting for the remaining N-1 lamps, the probability that there exists a way to apply the tool for M=32 several times and switch all the lamps off is positive and less than 0.0011%.
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Challenge:
02/28/2014 @ 01:00 PM EST
Solution:
04/03/2014 @ 01:00 PM EST
List Updated:
02/28/2014 @ 01:00 PM EST
People who answered correctly:
Dan Dima (02/28/2014 02:19 PM EDT)
Antoine Comeau (02/28/2014 05:22 PM EDT)
Radu-Alexandru Todor (02/28/2014 08:21 PM EDT)
Oleg Vlasii (02/28/2014 11:00 PM EDT)
Alexandre Gilotte (03/01/2014 12:13 PM EDT)
Alan Murray (03/01/2014 02:31 PM EDT)
Florian Fischer (03/01/2014 04:40 PM EDT)
Motty Porat (03/01/2014 05:21 PM EDT)
Lorenz Reichel (03/02/2014 11:10 AM EDT)
Jan Fricke (03/02/2014 12:31 PM EDT)
Olivier Mercier (03/02/2014 06:30 PM EDT)
Cynthia Beauchemin (03/03/2014 01:20 AM EDT)
Misha Lavrov (03/03/2014 09:33 AM EDT)
Joe Clark (03/03/2014 04:46 PM EDT)
Liubing Yu (03/03/2014 08:11 PM EDT)
David Friedman (03/04/2014 12:10 PM EDT)
Reiner Martin (03/04/2014 01:17 PM EDT)
Armin Krauss (03/04/2014 04:17 PM EDT)
Gilles-Philippe Paillé (03/04/2014 06:59 PM EDT)
Peter Gerritson (03/04/2014 07:42 PM EDT)
Joseph DeVincentis (03/05/2014 11:13 AM EDT)
Don Dodson & David Dodson (03/05/2014 02:22 PM EDT)
Xing Hu (03/07/2014 06:56 PM EDT)
Aharon Malachi (03/08/2014 08:18 AM EDT)
Mathias Schenker (03/08/2014 01:44 PM EDT)
Michael D. Schuresko (03/09/2014 06:13 PM EDT)
Álvaro Begué (03/10/2014 04:12 PM EDT)
Raj Kumar Pal (03/10/2014 05:39 PM EDT)
Uoti Urpala (03/11/2014 09:44 PM EDT)
John Tromp (03/12/2014 12:05 PM EDT)
Alex Fleischer (03/12/2014 02:05 AM EDT)
Gale Greenlee (03/15/2014 08:51 AM EDT)
Andrea Andenna (03/14/2014 02:52 PM EDT)
Markus Boettle (03/18/2014 10:05 AM EDT)
Chuck Carroll (03/18/2014 05:47 PM EDT)
Stefan Rüdrich (03/19/2014 09:47 AM EDT)
Todd Will (03/19/2014 01:07 PM EDT)
Daniel Bitin (03/19/2014 04:16 PM EDT)
Seung Hwan (Sonny) An (03/22/2014 09:16 AM EDT)
Philipp Seemann (03/23/2014 10:30 AM EDT)
Yewoon Choi (03/23/2014 10:40 AM EDT)
Michael Rosola (03/23/2014 10:53 AM EDT)
David Greer (03/23/2014 03:28 PM EDT)
Abhinav Kumar (03/24/2014 09:50 PM EDT)
Karthik Eswara (03/26/2014 12:53 AM EDT)
Stéphane Higueret (03/28/2014 01:34 PM EDT)
William Heller (03/29/2014 06:47 AM EDT)
Cindy Ji Won Lim (03/29/2014 10:45 AM EDT)
Jaesung Son (03/29/2014 06:56 PM EDT)
William Kang (03/29/2014 09:40 PM EDT)
Ehud Schreiber (03/30/2014 06:18 AM EDT)
David Yang (03/30/2014 10:27 AM EDT)
Hong Seongwoo (03/30/2014 08:47 AM EDT)
Daniel Nam (03/30/2014 08:51 PM EDT)
Peter Shim (03/30/2014 10:38 PM EDT)
Clive Tong (03/31/2014 01:51 AM EDT)
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