Ponder This

May 2016

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Ponder This Challenge:

Find two different ways to place chess pieces on an 8x8 board so that each square is threatened exactly the same number of times.
Note that we are using single color pieces and you can use as many pieces as you want (not limited to the standard chess set); but each square can hold at most one piece.
Supply your answer as two sets of 64 characters (k for king, q for queen, r for rook, b for bishop, n for knight; p for pawn, and = for empty square).
For example, on a 4x4 board, placing 4 queens as follows:
= q q =
= = = =
= = = =
= q q =
gives the following threats numbers:
2 2 2 2
2 3 3 2
2 3 3 2
2 2 2 2
There is another way to get to the same numerical solution as well.

Note that a chess piece does *not* threaten the square it is occupying (otherwise the problem would be too simple).

Update (02/05):

1. Find two different ways to place chess pieces on an 8x8 board so that each square is threatened exactly the same number of times, such that no piece is placed in the same position in both the boards, like the pair =qq= ==== ==== =qq= and ==== q==q q==q ==== in the 4x4 case; not a pattern that creates the same attack number for all the squares (like the trivial empty board).
2. Unlike real chess, the pieces are ignoring others in their way: attacking through them as in the 4x4 example.

Update (03/05):

1. To earn a '*', find a solution without using pawns; to get '**' find a solution using all other five pieces types (k,q,r,n,b).

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: 1/05/2016 @ 12:00 PM EST
Solution: 01/06/2016 @ 12:00 PM EST
List Updated: 29/05/2016 @ 12:00 PM EST

People who answered correctly:

*Robert Gerbicz (01/05/2016 05:57 PM IDT)
**Bert Dobbelaere (01/05/2016 11:57 PM IDT)
Jimmy Waters (02/05/2016 07:22 AM IDT)
Kang Jin Cho (02/05/2016 07:28 PM IDT)
*Rob Pratt (02/05/2016 08:12 PM IDT)
Frank Schoeps (02/05/2016 10:46 PM IDT)
**David F.H. Dunkley (02/05/2016 11:15 PM IDT)
Alexander Ruff (03/05/2016 01:34 AM IDT)
Benjamin Lui (03/05/2016 10:30 AM IDT)
Tamir Ganor (03/05/2016 11:08 AM IDT)
*János Csorba (03/05/2016 12:57 PM IDT)
*Vibhakar Shukla (03/05/2016 01:56 PM IDT)
*Arnab Bose (04/05/2016 01:07 AM IDT)
Radu-Alexandru Todor (04/05/2016 02:04 AM IDT)
Shirish Chinchalkar (04/05/2016 04:55 AM IDT)
Yan-Wu He (04/05/2016 05:09 AM IDT)
*Gary M. Gerken (04/05/2016 05:19 AM IDT)
Lorenz Reichel (04/05/2016 12:38 PM IDT)
Alon Elhanati (04/05/2016 12:42 PM IDT)
Bryce Fore (04/05/2016 06:22 PM IDT)
Tariq Ramlall (04/05/2016 08:29 PM IDT)
*Roberto Tauraso (04/05/2016 11:55 PM IDT)
Jacob Levinson (05/05/2016 12:34 AM IDT)
*Peter Gerritson (05/05/2016 01:57 AM IDT)
Clive Tong (05/05/2016 09:28 AM IDT)
Alex Fleischer (05/05/2016 05:48 PM IDT)
Edward Chu (05/05/2016 06:32 PM IDT)
*Lavanya Kannan (06/05/2016 07:45 AM IDT)
**Siddharth Joshi (06/05/2016 03:07 PM IDT)
Simon Uritsky (06/05/2016 11:27 PM IDT)
*Adrian Toncean (07/05/2016 07:50 PM IDT)
*Igor Karp (08/05/2016 05:56 AM IDT)
Cameron Ritson (09/05/2016 05:09 PM IDT)
*Stefano Leucci (09/05/2016 07:24 PM IDT)
Jesse Rearick (10/05/2016 02:40 AM IDT)
*Leandro Araújo (10/05/2016 11:07 AM IDT)
**Tom Sirgedas (10/05/2016 06:07 PM IDT)
Oleg Bogatchev (11/05/2016 12:55 AM IDT)
Daniel Chong Jyh Tar (11/05/2016 09:52 AM IDT)
*Liubing Yu (11/05/2016 10:52 AM IDT)
*Mark Beliaev (13/05/2016 12:00 AM IDT)
Hao Zheng (13/05/2016 03:05 PM IDT)
*Félix Breton (13/05/2016 05:39 PM IDT)
**Adrian Neacsu (13/05/2016 10:37 PM IDT)
**Christof Mroz (14/05/2016 03:01 AM IDT)
Joshua Durham (16/05/2016 09:54 PM IDT)
**Paolo Farinelli (17/05/2016 07:31 PM IDT)
**Wilder Boyden (18/05/2016 07:14 AM IDT)
**Peter Huggins (19/05/2016 10:49 AM IDT)
*Florian Fischer (21/05/2016 12:27 AM IDT)
*Sergey Koposov (25/05/2016 06:58 PM IDT)
*Pål Hermunn Johansen (27/05/2016 02:59 PM IDT)
Vladimir Dorofeev (28/05/2016 02:30 PM IDT)
**Casey Mihaloew (28/05/2016 05:28 PM IDT)
**Andreas Stiller (28/05/2016 09:37 PM IDT)
Erik Wünstel (31/05/2016 09:55 PM IDT)
David Greer (01/06/2016 11:04 AM IDT)