February 2012
Thank you, Kipp Johnson, for the wonderful challenge:
To decide who would play first in a human vs. computer game, the human suggested flipping a coin it produced from its pocket, stating “heads you win, tails I win.” The computer replied, “Humans are very devious. I know that your coin is not fair, and that the probability of heads on that coin is slightly less than one half. To make this perfectly fair, flip the coin repeatedly, and I win if the coin first shows heads on toss number 1, 14, 15, 19, 20, or 23. You win if it first shows heads on any other toss.”
If the computer is correct and p is the probability that the coin shows heads, give the best rational approximation to p with a denominator having fewer than 10 digits.
Bonus question: What is the significance of the six positions the computer chose?
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:
01/02/2012 @ 10:00 AM EST
Solution:
01/03/2012 @ 10:00 AM EST
List Updated:
01/01/2012 @ 10:00 AM EST
People who answered correctly:
* Also answered the bonus question correctly
Deron Stewart & Deane Stewart (02/01/2012 01:57 PM EDT)
Lu Wang (02/01/2012 02:37 PM EDT)
*Arthur Breitman (02/01/2012 03:04 PM EDT)
Adam Daire (02/01/2012 03:06 PM EDT)
Dan C (02/01/2012 03:17 PM EDT)
Denys Kopiychenko (02/01/2012 03:34 PM EDT)
Dan Dima (02/01/2012 03:45 PM EDT)
Hamidreza Bidar (02/01/2012 04:22 PM EDT)
Peter de Rivaz (02/01/2012 05:36 PM EDT)
*Sumanth Ravipati (02/01/2012 06:08 PM EDT)
Hakan Summakoglu (02/01/2012 06:35 PM EDT)
Hrushikesh Tilak (02/01/2012 06:38 PM EDT)
William Mantzel (02/01/2012 06:40 PM EDT)
Christian Blatter (02/01/2012 07:06 PM EDT)
*Donald Dodson (02/01/2012 07:36 PM EDT)
*Nick MmcGrath (02/02/2012 01:42 AM EDT)
*Erik Postma (02/02/2012 01:42 AM EDT)
Asaf Aharoni (02/02/2012 03:00 AM EDT)
Joël Bleuse (02/02/2012 02:18 PM EDT)
*Kevin Sham (02/02/2012 04:08 PM EDT)
Frederik Kaster (02/02/2012 04:59 PM EDT)
Greg Janée (02/02/2012 07:01 PM EDT)
Christopher Marks (02/02/2012 07:45 PM EDT)
*David S. Dodson (02/02/2012 10:22 PM EDT)
Mark Pervovskiy (02/02/2012 11:42 PM EDT)
Shilei Zang (02/03/2012 09:58 AM EDT)
Neil Fernandez (02/03/2012 12:02 PM EDT)
Rino Raj (02/03/2012 05:18 PM EDT)
*Sushanth Kodali (02/03/2012 08:17 PM EDT)
*Stéphane Higueret (02/03/2012 10:30 PM EDT)
Florin Spinu (02/03/2012 11:22 PM EDT)
Anton Sherwood (02/04/2012 02:29 AM EDT)
*Radu-Alexandru Todor (02/04/2012 09:39 AM EDT)
John Snyder (02/04/2012 02:29 PM EDT)
*Amos Guler (02/04/2012 03:37 PM EDT)
Diego Erdody (02/05/2012 03:09 AM EDT)
Peter Gerritson (02/05/2012 02:12 PM EDT)
Serge Thill (02/06/2012 11:46 AM EDT)
Dan Karliner (02/06/2012 02:55 PM EDT)
Michael Malak (02/06/2012 03:22 PM EDT)
*Clive Tong (02/06/2012 04:02 PM EDT)
Gale Greenlee (02/06/2012 04:29 PM EDT)
Stanislav Grudnitskiy (02/05/2012 05:09 AM EDT)
*Jason Crease (02/06/2012 10:39 PM EDT)
Daniel Bitin (02/07/2012 06:18 AM EDT)
Adrian Neacsu (02/07/2012 03:36 PM EDT)
Liubing Yu (02/07/2012 04:18 PM EDT)
*Chuck Carroll (02/07/2012 08:10 PM EDT)
Dejan Stakic (02/07/2012 08:41 PM EDT)
Chris Shannon (02/07/2012 10:48 PM EDT)
Gergely Pataki (02/08/2012 02:47 PM EDT)
Walter Schmidt (02/08/2012 04:03 PM EDT)
Hagen von Eitzen (02/08/2012 08:15 PM EDT)
*Rob Pratt (02/09/2012 08:35 PM EDT)
*Thomas Fleming (02/09/2012 10:54 PM EDT)
*Jonathan Namnath & Michael Kokosenski (02/10/2012 09:39 PM EDT)
*Joseph DeVincentis (02/11/2012 09:17 PM EDT)
Joaquim Neves Carrapa (02/11/2012 09:26 PM EDT)
Florian Fischer (02/12/2012 10:04 AM EDT)
Sergey Grishaev (02/12/2012 09:22 PM EDT)
Shouky Dan & Tamir Ganor (02/13/2012 09:35 AM EDT)
Ryan Milligan (02/13/2012 12:58 PM EDT)
*Karl D’Souza & Cristian Ianculescu (02/13/2012 01:07 PM EDT)
Bryan Wolf (02/13/2012 07:22 PM EDT)
*Chris Lewis (02/15/2012 09:10 AM EDT)
Thomas McHale (02/15/2012 11:55 PM EDT)
Mohammed M. Alokshiya (02/16/2012 05:26 AM EDT)
*Albert Stadler (02/16/2012 05:10 PM EDT)
Renato Negrinho (02/16/2012 09:53 PM EDT)
Radu Borza (02/17/2012 11:12 AM EDT)
Øyvind Grotmol (02/17/2012 05:36 PM EDT)
Eric Brasseur (02/18/2012 11:54 AM EDT)
Nanmuzi (02/19/2012 07:16 AM EDT)
M Zecevic (02/19/2012 09:14 AM EDT)
Harald Bögeholz (02/19/2012 04:26 PM EDT)
*Armin Krauss(02/20/2012 06:44 PM EDT)
Siva Dirisala (02/21/2012 06:47 AM EDT)
*Matthew D. Peavy (02/22/2012 04:49 AM EDT)
*Arthur Vause (02/23/2012 02:06 PM EDT)
Fletcher Dostie (02/23/2012 04:03 PM EDT)
Allen Sirolly (02/26/2012 06:49 PM EDT)
Rod Carvalho (02/27/2012 12:23 AM EDT)
Anoop Varghese (02/27/2012 10:25 AM EDT)
Chidambaram Annamalai (02/28/2012 05:05 AM EDT)
*Mathias Schenker (02/28/2012 12:39 PM EDT)
Todd Will (02/28/2012 04:06 PM EDT)
Dan Kneezel (02/29/2012 06:12 AM EDT)
Nitish Chandran (02/29/2012 07:31 AM EDT)
*Andreas Razen (02/29/2012 05:48 PM EDT)
Edgardo Deza (02/29/2012 10:18 PM EDT)
Attention: If your name is posted here and you wish it removed please send email to the ponder@il.ibm.com.