IBM Research | Ponder This | December 2011 challenges

Ponder This

December 2011

<<November December January>>

Ponder This Challenge:

This month's challenge is by Martin Erickson (thanks).

Two players (White and Black) are playing on an infinite chess board (extending infinitely in all directions).

First, White places a certain number of queens (and no other pieces) on the board.

Black then places a king on any unoccupied, unattacked square of the board.

Both players take turns moving until Black is checkmated.

What is the minimum number of queens White needs to force a checkmate?

Answer the same problem if White starts with rooks instead of queens.

Do the same for bishops and knights.

Let Q, R, B, and N be the minimum number of queens, rooks, bishops, and knights, respectively. What is the sum 1/Q + 1/R + 1/B + 1/N?

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: 12/01/2011 @ 10:00 AM EST
Solution: 01/01/2012 @ 10:00 AM EST
List Updated: 12/01/2011 @ 10:00 AM EST

Aaron Matthews (11/29/2011 05:32 AM EDT)
Hari MP (11/29/2011 08:23 AM EDT)
Dan Dima (11/29/2011 07:55 PM EDT)
Jan Fricke (11/30/2011 12:26 PM EDT)
Christopher Marks (11/30/2011 03:32 PM EDT)
Joseph DeVincentis (12/01/2011 12:29 PM EDT)
Joshua Gunderson (12/01/2011 06:42 PM EDT)
Luke Pebody (12/01/2011 07:56 AM EDT)
Rafael Rabin (12/01/2011 11:00 AM EDT)
Aviv Nisgav (12/01/2011 01:00 PM EDT)
Andrew D Kidd (12/01/2011 04:23 PM EDT)
Chuck Carroll (12/01/2011 08:40 PM EDT)
Peter and Jenny de Rivaz (12/01/2011 10:12 PM EDT)
Victor Chang (12/02/2011 05:08 AM EDT)
Kevin Berk (12/02/2011 07:20 PM EDT)
Panos Tsikogiannopoulos (12/03/2011 05:51 AM EDT)
Reinder Verlinde (12/03/2011 12:11 PM EDT)
Jochen Hoenicke (12/03/2011 05:28 PM EDT)
Forest Deal (12/04/2011 01:18 AM EDT)
Shmuel Menachem Spiegel (12/04/2011 04:09 AM EDT)
Dmitry Litvinenko (12/04/2011 02:53 PM EDT)
Rajendran Thirupugalsamy (12/04/2011 02:56 AM EDT)
Gale Greenlee (12/04/2011 09:56 PM EDT)
Joe Riel (12/04/2011 10:54 PM EDT)
Leon Smith (12/02/2011 02:28 PM EDT)
Robin Ryder (12/05/2011 11:07 AM EDT)
David Greer (12/05/2011 12:14 PM EDT)
Radu-Alexandru Todor & Andreas Razen (12/05/2011 01:47 PM EDT)
Ariel Flat (12/05/2011 02:58 PM EDT)
Walter Schmidt (12/02/2011 03:06 PM EDT)
Thomas Pensyl & Samuel Thomsen (12/05/2011 07:40 PM EDT)
Tom Sirgedas (12/05/2011 07:40 PM EDT)
Anees Shaikh (12/06/2011 05:20 AM EDT)
Christophe Malherbe (12/06/2011 10:40 AM EDT)
Wu Chengyuan (12/06/2011 11:12 AM EDT)
Adam Daire (12/06/2011 02:43 PM EDT)
Tristan Jong (12/07/2011 01:23 AM EDT)
Nick McGrath (12/07/2011 12:02 PM EDT)
Amit Bhatia (12/07/2011 06:40 PM EDT)
Yaron Gvili (12/08/2011 12:50 AM EDT)
V.P.Gohil & P.B. Trivedi (12/08/2011 07:24 AM EDT)
Kipp Johnson & John Brunecz (12/08/2011 08:25 PM EDT)
Emanuele Natale (12/08/2011 09:39 PM EDT)
Max Nepokroeff (12/08/2011 10:17 PM EDT)
Amit Bhatia (12/11/2011 02:45 PM EDT)
Adrian Neacsu (12/11/2011 02:45 PM EDT)
Chris Kittlitz (12/12/2011 06:22 PM EDT)
Adrian Kummer (12/12/2011 08:52 PM EDT)
Thomas Rohr (12/13/2011 04:07 PM EDT)
Karine Mandervelde (12/14/2011 10:31 AM EDT)
Chris Lewis (12/14/2011 12:00 PM EDT)
Deron Stewart (12/14/2011 04:51 PM EDT)
Liubing Yu (12/15/2011 03:53 PM EDT)
John Tromp (12/15/2011 04:25 PM EDT)
Yash Kochar (12/16/2011 05:01 PM EDT)
Edward Kim (12/16/2011 09:19 PM EDT)
Subbu Devulapalli (12/18/2011 09:19 PM EDT)
Jeff Steele (12/18/2011 11:03 PM EDT)
M Zecevic (12/19/2011 12:41 PM EDT)
Traian Delca (12/23/2011 10:01 AM EDT)
Frank Marrs (12/23/2011 10:55 AM EDT)
Maris Van Sprang (12/26/2011 07:29 AM EDT)
Shilei Zang (12/26/2011 06:52 PM EDT)
Sergey Grishaev & Denys Kopiychenko (12/27/2011 09:18 PM EDT)
Mark Pervovskiy (12/27/2011 09:10 PM EDT)
Naftali Peles (12/30/2011 03:10 AM EDT)
Kshitij Gajjar (12/30/2011 07:37 PM EDT)
Kevin Williamson (12/31/2011 06:51 PM EDT)

Attention: If your name is posted here and you wish it removed please send email to the ponder@il.ibm.com.