IBM Research | Ponder This | November 2007 challenges

# Ponder This

## November 2007

<<October November December>>

Ponder This Challenge:

K light-emitting points are placed on a three-dimensional integer lattice (N*N*N cube). Three spectators observe these lights from three different perspectives. Each of them watches a projection on two of three coordinates: XY; YZ; and ZX. For example, the first observer sees the point (2,7,3) as (2,7); the second sees it as (7,3); and the third as (3,2).

A set of light points is defined as revealing if given any point (u,v) in the N*N square, there is an observer who sees a light at that point in his projection and one can uniquely reveal both the exact source of light and the identity of the observer: each point of light (u,v) is seen by exactly one spectator and he or she sees it exactly once (no light hides behind another light).

For which N is there a revealing set? Show how to construct such a set for all feasible N and prove the nonexistence of them for all other N.

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: 11/01/2007 @ 12:00 PM EDT
Solution: 12/03/2007 @ 05:15 PM EDT
List Updated: 12/06/2007 @ 05:30 PM EDT

Balakrishnan V (11.01.2007 @05:05:01 PM EDT)
Dan Dima (11.01.2007 @05:10:31 PM EDT)
Mirco Pötter (11.01.2007 @06:15:44 PM EDT)
Luke Pebody (11.01.2007 @07:02:28 PM EDT)
Andreas Eisele (11.02.2007 @04:13:05 AM EDT)
Alan O'Donnell (11.02.2007 @10:37:05 AM EDT)
Alan Murray (11.02.2007 @01:03:52 PM EDT)
Christian Blatter (11.04.2007 @01:57:24 PM EDT)
José H. Nieto (11.04.2007 @08:49:02 PM EDT)
Frank Yang (11.05.2007 @11:55:27 AM EDT)
John T. Robinson (11.05.2007 @02:29:28 PM EDT)
Udi Aharoni (11.06.2007 @10:09:08 AM EDT)
Jiri Navratil (11.06.2007 @12:50:40 AM EDT)
Michael Quist (11.06.2007 @09:45:22 PM EDT)
Qurqirish Dragon (11.06.2007 @12:44:47 PM EDT)
Daniel Bitin (11.08.2007 @05:30:53 AM EDT)
Benedikt Engels (11.08.2007 @06:38:13 AM EDT)
Alan McLoughlin (11.08.2007 @11:31:43 AM EDT)
John Ritson (11.09.2007 @04:46:52 PM EDT)
Kevin Williamson (11.11.2007 @08:01:31 AM EDT)
gmgerken (11.11.2007 @12:05:54 AM EDT)
Andrea Andenna (11.11.2007 @04:31:25 PM EDT)
John G. Fletcher (11.12.2007 @12:07:37 AM EDT)
Maxim G. Smith (11.15.2007 @02:45:55 PM EDT)
Ole Martin (11.16.2007 @02:57:56 AM EDT)
Andrew Buchanan (11.16.2007 @07:28:33 AM EDT)
Hongcheng Zhu (11.18.2007 @03:51:28 AM EDT)
Huicheng Guo (11.18.2007 @11:44:39 PM EDT)
David McQuillan (11.20.2007 @05:33:21 AM EDT)
Wu Hao (11.23.2007 @06:12:02 AM EDT)
Wolfgang Kais (11.24.2007 @05:30:20 AM EDT)
Gale Greenlee (11.24.2007 @04:35:33 PM EDT)
David Friedman (11.26.2007 @05:59:18 PM EDT)
Dion Harmon (11.27.2007 @12:24:59 PM EDT)
Phil Muhm (11.27.2007 @05:57:45 PM EDT)
Reiner Martin (11.30.2007 @07:24:47 PM EDT)
Shmuel Menachem Spiegel (12.01.2007 @07:03:01 PM EDT)

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