Puzzle
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Ponder This Challenge - March 2009 - Hexadecimal exercise

Ponder This Challenge:

Because February's challenge was very difficult, we postponed the submission deadline by a month and we'll post the solution on April 1st. In the meantime, here is a more straightforward challenge:

There are several simultaneous solutions for the following two exercises (the second is a 90-degree rotation of the first):

  a b c      g d a
+         +
  d e f      h e b   
  =====      ===== 
  g h i      i f c

One of them is

5 8|3
   |
1 4|6
===+=
7 2|9

Our challenge is to find a similar exercise in hexadecimal.

One can prove that a 4x4 is insolvable, so we added a few zeros and ask you to fit all 15 nonzero hexadecimal digits in

  abcde       mjfa
+ fghi0       nkgb
  jk00l     + 00hc 
  =====       00id
  mn00o       ====
              ol0e

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

  • By using modulo-15 arithmetic, one can save some computations and find the only possible solution:

    6a8b3
    4e750
    1900c
    d200f

Solvers

  • Gary M. Gerken (02/28/2009 12:51 AM EDT)
  • Peter Mattsson (02/28/2009 01:42 PM EDT)
  • Ioan Marius Popdan (02/28/2009 08:26 PM EDT)
  • Sangxia Huang (03/01/2009 03:19 AM EDT)
  • Al Zimmermann (03/01/2009 05:53 AM EDT)
  • Are Hjørungnes (03/01/2009 07:20 AM EDT)
  • John G. Fletcher (03/01/2009 06:22 PM EDT)
  • Balakrishnan V (03/01/2009 06:38 PM EDT)
  • Oscar Portela (03/01/2009 07:15 PM EDT)
  • Nyles Heise (03/01/2009 09:10 PM EDT)
  • Bernardino Romera Paredes (03/01/2009 09:27 PM EDT)
  • John T. Robinson (03/01/2009 11:17 PM EDT)
  • Steven Langerwerf (03/01/2009 12:58 PM EDT)
  • Amos Guler (03/01/2009 03:48 PM EDT)
  • Andreas Eisele (03/02/2009 12:33 AM EDT)
  • Michael Brand (03/02/2009 04:47 AM EDT)
  • Fabio Filatrella (03/02/2009 05:41 AM EDT)
  • Vladimir Sedach (03/02/2009 08:15 AM EDT)
  • Albert Stadler (03/02/2009 08:56 AM EDT)
  • Chris Lomont (03/02/2009 01:27 PM EDT)
  • Arthur Breitman (03/02/2009 01:43 PM EDT)
  • Dan Dima (03/02/2009 03:43 PM EDT)
  • Adam Daire (03/02/2009 05:00 PM EDT)
  • Dan Wood (03/02/2009 08:45 PM EDT)
  • Thomas Buchholz (03/02/2009 08:50 PM EDT)
  • Mauro Bampo (03/03/2009 10:28 AM EDT)
  • Dmitry Litvinenko (03/03/2009 11:40 AM EDT)
  • Fred Schalekamp (03/03/2009 11:40 AM EDT)
  • Igor Malashkin (03/03/2009 03:42 PM EDT)
  • Ashutosh Mehra (03/03/2009 12:54 PM EDT)
  • Harold Gutch (03/03/2009 05:42 PM EDT)
  • Chris Shannon (03/03/2009 06:15 PM EDT)
  • Don Dodson (03/03/2009 06:27 PM EDT)
  • Clive Tong (03/04/2009 06:19 AM EDT)
  • Muralidhar Seshadri (03/04/2009 06:12 PM EDT)
  • Tom Sirgedas (03/04/2009 08:22 PM EDT)
  • Jesse Kolman (03/05/2009 01:20 AM EDT)
  • Steffen Wolf (03/05/2009 11:09 AM EDT)
  • Bobby Brennan (03/05/2009 12:36 PM EDT)
  • Kalyana Chakravarthy (03/06/2009 01:15 AM EDT)
  • Michael Liepelt (03/06/2009 12:43 PM EDT)
  • Yuho Chu (03/06/2009 11:39 PM EDT)
  • David Hentrich (03/07/2009 06:33 PM EDT)
  • Michael Wegener (03/08/2009 05:36 PM EDT)
  • Tim Nordenfur (03/08/2009 08:15 PM EDT)
  • Guy Tannenbaum (03/09/2009 03:49 AM EDT)
  • Muharrem Görkem (03/09/2009 06:45 PM EDT)
  • Greg Janee (03/10/2009 12:04 AM EDT)
  • Benjamin Bachmann (03/10/2009 11:27 AM EDT)
  • Travis Meyer (03/10/2009 08:58 PM EDT)
  • Bradley Wild (03/11/2009 11:26 AM EDT)
  • Alex Taylor (03/11/2009 01:25 PM EDT)
  • David Friedman (03/11/2009 03:02 PM EDT)
  • Neil Smeby (03/11/2009 07:25 PM EDT)
  • Daniel Chong Jyh Tar (03/12/2009 12:50 AM EDT)
  • Michael van Fondern (03/12/2009 03:43 AM EDT)
  • Jochen Klein (03/13/2009 07:41 AM EDT)
  • Mark Buisseret (03/14/2009 05:53 PM EDT)
  • Bojan Basic (03/14/2009 06:35 PM EDT)
  • Nagendra Gulur Dwarakanath (03/16/2009 10:34 AM EDT)
  • Kin Keung Ma (03/16/2009 10:25 PM EDT)
  • Boris Nikolaus (03/17/2009 07:17 PM EDT)
  • Gaurav Raizada and Sourabh Agrawal (03/18/2009 10:16 AM EDT)
  • Nick Miller (03/20/2009 01:45 PM EDT)
  • Raj Mohan (03/22/2009 01:45 AM EDT)
  • Daniel Bitin (03/22/2009 10:42 AM EDT)
  • Nagy Zoltan (03/22/2009 08:42 PM EDT)
  • Samuel Schwager (03/23/2009 11:57 AM EDT)
  • Mihai Cioc (03/23/2009 07:30 PM EDT)
  • Adriana Clerici (03/26/2009 01:23 PM EDT)
  • Bob DiMarco (03/26/2009 02:57 PM EDT)
  • Pritpal Ahuja (03/27/2009 11:53 AM EDT)
  • Siva Dirisala (03/27/2009 09:45 PM EDT)
  • Francois Galilee (03/28/2009 09:05 AM EDT)
  • Wei Shi (03/29/2009 03:45 AM EDT)
  • Stéphane Higueret (03/30/2009 08:38 AM EDT)

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