IBM Research | Ponder This | October 2005 challenges

# Ponder This

## October 2005

<<September October November>>

Ponder This Challenge:

Puzzle for October 2005.

This months puzzle concerns arrays of integers, a(i,j) with the following property.  For all pairs of distinct rows i1,i2 and distinct columns j1,j2 the diagonal sum a(i1,j1)+a(i2,j2) and the anti-diagonal sum a(i1,j2)+a(i2,j1) are unequal.  We are interested in finding such arrays with the entries chosen from as narrow a range of integers as possible.  For example the following is an example of such a 3x3 array with entries chosen from {0,1}

0  0  1
0  1  0
1  0  0

Find a 5x5 array with this property with entries chosen from {0,1,2}. If this is too easy try to find a 7x7 array with entries from {0,1,2,3,4}, a 11x11 array with entries from {0,1,...,6,7} and a 13x13 arrays with entries from {0,1,...,7,8}.  This will probably require computer assistance.

The first 100 people who answer all four parts correctly will be listed. The answer will be posted a week after the 100th is received, or at the end of the month.

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: 10/01/2005 @ 08:30 AM EST
Solution: 11/01/2005 @ 08:30 AM EST
List Updated: 10/01/2005 @ 08:30 AM EST

Chuck Carroll (10.01.2005 @03:11:11 PM EDT)
Wolfgang Kais (10.03.2005 @07:07:00 PM EDT)
Daniel Bitin (10.04.2005 @08:29:17 AM EDT)
Eugene Vasilchenko (10.05.2005 @12:52:44 AM EDT)
Marco Rolando (10.05.2005 @05:25:01 AM EDT)
Ardian Kristanto Poernomo (10.05.2005 @02:43:36 PM EDT)
Yong Liu (10.05.2005 @03:37:11 PM EDT)
Rohit Das (10.05.2005 @06:28:15 PM EDT)
John Hubenschmidt (10.06.2005 @02:14:14 PM EDT)
Bertram Felgenhauer (10.06.2005 @11:57:23 PM EDT)
Michael Brand (10.07.2005 @10:01:40 AM EDT)
Emile Joubert (10.07.2005 @10:49:35 AM EDT)
V. Balakrishnan (10.08.2005 @12:34:38 AM EDT)
Viktor Medvedev (10.10.2005 @12:08:37 AM EDT)
Robert Benea (10.10.2005 @04:28:42 AM EDT)
David Friedman (10.10.2005 @12:32:53 PM EDT)
Raicho Tchalkov (10.11.2005 @05:14:07 AM EDT)
Kalyana Chakravarthy (10.11.2005 @01:02:11 PM EDT)
Dave Biggar (10.12.2005 @01:00:15 AM EDT)
Dharmadeep Muppalla (10.12.2005 @01:33:24 AM EDT)
Piotr Zielinski (10.12.2005 @10:58:09 AM EDT)
Tom Sirgedas (10.12.2005 @06:11:27 PM EDT)
Patrick Beebe (10.12.2005 @06:49:02 PM EDT)
Kin Keung Ma (10.13.2005 @01:13:21 PM EDT)
Bin Zhao (10.13.2005 @02:16:23 AM EDT)
John G. Fletcher (10.13.2005 @11:44:45 PM EDT)
Se Kwon Kim (10.16.2005 @04:15:59 AM EDT)
Ashutosh Mahajan (10.17.2005 @07:16:35 PM EDT)
Kennedy and Slick (10.18.2005 @01:54:39 AM EDT)
Zdenek Spacek (10.18.2005 @07:28:51 PM EDT)
Shawn Simister (10.19.2005 @12:43:25 AM EDT)
Vinay Gupta (10.20.2005 @09:18:19 AM EDT)
Lucas Galfaso (10.26.2005 @02:54:15 AM EDT)
Oleg Trott (10.27.2005 @09:28:52 AM EDT)
Patricio Alva (10.27.2005 @05:39:35 PM EDT)
Ananda Raidu (10.28.2005 @10:33:51 AM EDT)
Devin Myers (10.28.2005 @11:43:37 AM EDT)
Max Alekseyev (10.29.2005 @08:56:38 AM EDT)
Liubing Yu (10.31.2005 @09:36:47 AM EDT)
DaiLiang (10.31.2005 @09:02:15 PM EDT)

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