IBM Research | Ponder This | January 2015 challenges
Skip to main content

Ponder This

January 2015

<<December January February>>


Ponder This Challenge:


Kakuro is a numeric crossword puzzle, in which each square occurs in exactly two definitions: vertical and horizontal. Each definition is on the sum of at least two squares and each "word" is a set of different non-zero digits.

It is easy to see that we can omit any single definition without losing any information, but omitting two definitions may enlarge the set of possible solutions.


This month's challenge is to design a small Kakuro puzzle which is uniquely solvable, but for which removing any two definitions introduces at least one more solution.

For example, a 2*3 matrix where the sums of the two rows are 7 and 9 and the sums of the three columns are 3, 6, and 7 is not uniquely solvable. Please provide the solution as lines of sum and a list of cell coordinates.

The example above in this format would look like

7 A1 A2 A3
9 B1 B2 B3
3 A1 B1
6 A2 B2
7 A3 B3



Update (01/03): Bonus '*' for a non rectangular Kakuro.
The missing definitions should still be legal (all different 1-9 digits).


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: 12/31/2014 @ 12:00 PM EST
Solution: 02/01/2015 @ 12:00 PM EST
List Updated: 12/31/2014 @ 12:00 PM EST

People who answered correctly:

Lorenz Reichel (12/31/2014 01:39 PMEDT)
Aviv Nisgav (12/31/2014 03:15 PM EDT)
Gyozo Nagy (12/31/2014 07:44 PM EDT)
Amos Guler (12/31/2014 07:50 PM EDT)
Joseph DeVincentis (01/01/2015 05:24 AM EDT)
Graham Hemsley (01/01/2015 06:44 AM EDT)
Hendrik Nigul (01/01/2015 12:49 PM EDT)
Arthur Vause (01/01/2015 03:27 PM EDT)
Tad White (01/01/2015 05:14 PM EDT)
*Motty Porat (01/01/2015 06:11 PM EDT)
Dan Dima (01/01/2015 06:19 PM EDT)
Yury Sobolev (01/01/2015 10:37 PM EDT)
Louis Slothouber (01/01/2015 11:42 PM EDT)
Yue Ru Sun (01/02/2015 03:42 AM EDT)
William Heller (01/02/2015 09:53 PM EDT)
*James Dow Allen (01/03/2015 08:48 AM EDT)
Dieter Beckerle (01/04/2015 01:22 PM EDT)
Kang Jin Cho (01/04/2015 02:33 PM EDT)
*Oleg Vlasii (01/05/2015 03:24 AM EDT)
*Kang Jin Cho (01/05/2015 01:07 PM EDT)
*Donald Dodson (01/05/2015 01:37 PM EDT)
Harald Bögeholz (01/05/2015 04:21 PM EDT)
Liubing Yu (01/06/2015 12:51 AM EDT)
Arsene Lui (01/06/2015 01:06 AM EDT)
Shouky Dan & Tamir Ganor (01/06/2015 09:30 AM EDT)
*Arthur Vause (01/06/2015 10:10 AM EDT)
*Dieter Beckerle (01/06/2015 12:06 PM EDT)
Julian M (01/06/2015 03:03 PM EDT)
*Andreas Stiller (01/06/2015 04:16 PM EDT)
Chuck Carroll (01/06/2015 08:16 PM EDT)
Tommi Lindgren (01/07/2015 03:00 PM EDT)
Mariia Mykhailova (01/07/2015 07:46 PM EDT)
*Igor Novak (01/07/2015 11:08 PM EDT)
Lucas Mirelmann (01/09/2015 12:42 PM EDT)
Shirish Chinchalkar (01/10/2015 10:23 AM EDT)
Mathias Schenker (01/11/2015 04:24 PM EDT)
*Sean Egan (01/12/2015 05:01 PM EDT)
*Joseph Berman (01/13/2015 01:34 PM EDT)
*Cody Pfau (01/13/2015 07:13 PM EDT)
*Taisiya Izhutkina (01/14/2015 10:23 PM EDT)
*Armin Krauss (01/15/2015 08:39 AM EDT)
Mathias Schenker (01/15/2015 08:52 AM EDT)
*Franciraldo Cavalcante (01/15/2015 05:56 PM EDT)
Vladimir Dorofeev (01/16/2015 08:50 AM EDT)
*Dan Ismailescu (01/16/2015 03:29 PM EDT)
Konstantin Dzhigardzhyan (01/17/2015 11:18 AM EDT)
*Mark Pervovskiy (01/17/2015 09:57 PM EDT)
*Daniel Bitin (01/18/2015 10:43 AM EDT)
*David Greer (01/21/2015 02:41 AM EDT)
*Teodora Baeva (01/21/2015 10:19 AM EDT)
Thomas Chaperon (01/21/2015 08:14 PM EDT)
Emilio Del Tessandoro (01/22/2015 01:21 PM EDT)
*Li Li (01/22/2015 04:14 PM EDT)
*Hyun Jin Kim (01/25/2015 02:03 PM EDT)
*Jhiseung Daniel Hahn (01/25/2015 03:01 PM EDT)
*Yujin Kim (01/25/2015 06:08 PM EDT)
*Seung Hwan (Sonny) An (01/25/2015 06:16 PM EDT)
Jim Miles (01/26/2015 05:52 PM EDT)
*Kwonil Kobe Ko (01/27/2015 04:48 PM EDT)
*Chaeyeon Oh (01/27/2015 08:18 PM EDT)
Gerriet Moehlmann (01/28/2015 03:14 AM EDT)
Hyun Jae Moon (01/28/2015 10:34 AM EDT)
Michel Hannoyer (01/28/2015 09:26 PM EDT)
*Florian Fischer (01/30/2015 09:20 PM EDT)
*William Kang (01/31/2015 12:44 PM EDT)
*Peter Shim (01/31/2015 04:26 PM EDT)
*SeongKweon (Alex) Hong (01/31/2015 05:53 PM EDT)
Gilles-Philippe Paillé (01/31/2015 07:32 PM EDT)
*Robin Injoo Park (01/31/2015 08:33 PM EDT)
Michael Schuresko (02/01/2015 06:30 AM EDT)
Kyoung Lee (02/01/2015 12:14 AM EDT)
Todd Will (02/01/2015 03:39 PM EDT)
Nell Kopel (02/01/2015 02:05 PM EDT)


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