Ponder This Challenge - September 2008 - Partitioning 13x13 to squares

Ponder This Challenge:

Consider a 13x13 checkerboard. It can be partitioned into a collection of smaller square checkerboards in various ways. For example into 169 1x1 checkerboards or into 1 12x12 and 25 1x1 checkerboards. What is the minimum number of smaller square checkerboards that a 13x13 checkerboard can be partitioned into? Show how this can be done. Note we are not asking for (and will not supply) a proof of minimality.

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

Solution

• Click here to view the solution

  The minimum number is 11 as illustrated below. This problem is from Sam Loyd via Martin Gardner.

  1111111AAAAAA
  1111111AAAAAA
  1111111AAAAAA
  1111111AAAAAA
  1111111AAAAAA
  1111111AAAAAA
  1111111244455
  BBBBBB3344455
  BBBBBB3344466
  BBBBBB7777866
  BBBBBB7777999
  BBBBBB7777999
  BBBBBB7777999

  ---

  If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com

Solvers

• Dan Dima (09.04.2008 @02:43 PM EDT)
• V Balakrishnan (09.04.2008 @03:28 PM EDT)
• Albert Stadler (09.04.2008 @02:15 PM EDT)
• Bojan Basic (09.04.2008 @02:35 PM EDT)
• Alan O'Donnell (09.04.2008 @01:59 PM EDT)
• Andreas Eisele (09.04.2008 @05:32 PM EDT)
• Raul Blazquez (09.04.2008 @06:37 PM EDT)
• Sangita Ukil & Abhisek Ukil (09.04.2008 @08:14 PM EDT)
• Gale Greenlee (09.05.2008 @12:17 AM EDT)
• Zhou Guang (09.05.2008 @02:19 AM EDT)
• Dan Colestock (09.05.2008 @02:32 AM EDT)
• Andreas Gruen (09.05.2008 @10:55 AM EDT)
• Harald Boegeholz (09.05.2008 @11:15 AM EDT)
• Gary M. Gerken (09.05.2008 @11:31 AM EDT)
• Henry Bottomley (09.05.2008 @11:38 AM EDT)
• Michael Schaaf (09.05.2008 @01:21 PM EDT)
• Farid Lian (09.05.2008 @04:36 PM EDT)
• John Tromp and Alvaro Begue (09.05.2008 @04:41 PM EDT)
• Arthur Breitman (09.05.2008 @07:07 PM EDT)
• Lego Haryanto (09.05.2008 @08:47 PM EDT)
• David Barr (09.06.2008 @07:36 AM EDT)
• Fred Schalekamp (09.06.2008 @09:57 AM EDT)
• Krunoslav Kovac (09.06.2008 @12:01 AM EDT)
• Mathias Schenker (09.06.2008 @03:25 PM EDT)
• Simon Frettloeh (09.06.2008 @04:47 PM EDT)
• Maris van Sprang (09.06.2008 @04:47 PM EDT)
• Arno Candel (09.06.2008 @06:24 PM EDT)
• Michael Liepelt (09.07.2008 @11:56 AM EDT)
• Joseph DeVincentis (09.07.2008 @08:04 PM EDT)
• Andreas Stiller (09.07.2008 @08:20 PM EDT)
• Radu Borza (09.07.2008 @12:44 PM EDT)
• Karthik Kumar (09.08.2008 @06:12 AM EDT)
• Gergely Pataki (09.08.2008 @04:26 PM EDT)
• Reiner Martin (09.08.2008 @06:01 PM EDT)
• Frank Vernaillen (09.08.2008 @06:29 PM EDT)
• Stephen Merriman (09.08.2008 @07:37 AM EDT)
• Daniel Hsu (09.08.2007 @07:58 PM EDT)
• Jack Kennedy (09.08.2008 @12:54 PM EDT)
• L J Zigerall Jr (09.09.2008 @02:10 AM EDT)
• Aleksandar Damnjanovic (09.09.2008 @12:08 AM EDT)
• Eugene Vasilchenko (09.09.2008 @05:26 PM EDT)
• Anthony P Jones (09.10.2008 @09:43 PM EDT)
• Daniel Bitin (09.10.2008 @12:36 PM EDT)
• Amos Guler (09.11.2008 @01:19 PM EDT)
• Luke Pebody (9.11.2008 @05:57 PM EDT)
• Joaquim Carrapa (9.11.2008 @06:57 PM EDT)
• Raphael Finkel (9.12.2008 @06:22 AM EDT)
• Chuck Grant (9.12.2008 @10:32 AM EDT)
• Mate Bartalos (9.12.2008 @05:30 AM EDT)
• Cobus de Waal (9.12.2008 @06:09 AM EDT)
• Alex Wagner (9.12.2008 @08:41 PM EDT)
• Sinisa Popovic (9.13.2008 @09:08 AM EDT)
• George McCarthy (9.13.2008 @09:09 AM EDT)
• Catalin Buzoiu (9.13.2008 @05:46 PM EDT)
• Jesse Kolman (9.13.2008 @07:25 PM EDT)
• Rani Hod (9.14.2008 @09:56 AM EDT)
• Christian Pape (9.14.2008 @01:23 PM EDT)
• Nicolas Wu (9.15.2008 @01:18 PM EDT)
• Karthik Kalyanam (9.15.2008 @11:51 PM EDT)
• Victor Chang (9.16.2008 @02:54 AM EDT)
• Dave Parashar (9.16.2008 @08:29 AM EDT)
• Fabio Filatrella (9.16.2008 @10:57 AM EDT)
• Andrew Rochon (9.16.2008 @09:37 PM EDT)
• Benjamin Bachmann (9.17.2008 @08:54 AM EDT)
• Kalle Matias Leppele (9.18.2008 @09:27 AM EDT)
• Donald T. Dodson (9.18.2008 @03:25 PM EDT)
• Ioan Marius Popdan (9.19.2008 @10:32 AM EDT)
• Jiri Navratil (9.19.2008 @01:57 PM EDT)
• Nyles Heise (9.20.2008 @12:30 AM EDT)
• John G. Fletcher (9.20.2008 @02:09 PM EDT)
• Boris Nikolaus (09.22.2008 @05:02 PM EDT)
• Kali Gajula and Ramteke Mithil (09.24.2008 @05:36 AM EDT)
• Ranjit Eswaran (09.24.2008 @05:44 AM EDT)
• David Gower (09.24.2008 @09:45 AM EDT)
• Tinglekar Srinath (09.24.2008 @12:36 PM EDT)
• Robert Sarvis (9.25.2008 @01:47 PM EDT)
• Gurunandan Pai (9.26.2008 @06:41 AM EDT)
• Thomas Rohr (9.26.2008 @07:42 AM EDT)
• Andrea Andenna (9.28.2008 @04:17 AM EDT)
• Jampani Kv Raju (9.30.2008 @03:03 AM EDT)
• Alexandru Nicau (9.30.2008 @07:49 AM EDT)