October 2018 - Challenge

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This month's challenge is by a frequent solver, Bert Dobbelaere. (Thanks!)

Put N points on integer coordinates of a rectangular grid of dimension L1xL2, so that no three points are collinear and the areas of the triangles formed by the C(N,3) possible triplets are all different.

For example, for N=4 and L1=L2=3, the following set of points is a solution: [[1,0],[1,1],[0,3],[3,3]]

The areas formed by the 4 triangles are:

[1, 0] [1, 1] [0, 3] 0.5
[1, 0] [1, 1] [3, 3] 1
[1, 0] [0, 3] [3, 3] 4.5
[1, 1] [0, 3] [3, 3] 3

Find a solution for N=11 and the L1*L2<=600.

You can play a game of a simple version of the challenge here.


A bonus '*' will be awarded to the solutions with the smallest area.




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: 26/09/2018 @ 12:00 PM EST
Solution: 02/11/2018 @ 12:00 PM EST
List Updated: 02/11/2018 @ 12:00 PM EST

People who answered correctly:

Harald Bögeholz (30/09/18 09:21 AM IDT)
Oleg Vlasii (02/10/18 07:44 AM IDT)
Vladimir Volevich (04/10/18 01:07 PM IDT)
Dominik Reichl (04/10/18 11:22 PM IDT)
Shirish Chinchalkar (05/10/18 02:31 AM IDT)
Kang Jin Cho (06/10/18 11:39 AM IDT)
Mark Mammel & Jean-Charles Meyrignac (07/10/18 03:26 PM IDT)
mtve (07/10/18 07:23 PM IDT)
Serge Batalov (09/10/18 05:26 PM IDT)
Markus Sigg (10/10/18 09:27 AM IDT)
Alper Halbutogullari (11/10/18 02:46 PM IDT)
Andreas Stiller (12/10/18 11:53 AM IDT)
Arthur Vause (13/10/18 10:27 AM IDT)
Pål Hermunn Johansen (15/10/18 10:26 AM IDT)
Benjamin Buhrow (15/10/18 03:35 PM IDT)
Arthur Vause (16/10/18 10:38 AM IDT)
Florian Fischer (16/10/18 11:19 PM IDT)
*Hermann Jurksch (19/10/18 07:08 PM IDT)
Michael Liepelt (21/10/18 07:57 AM IDT)
Hugo Pfoertner (22/10/18 07:11 AM IDT)
Daniel Bitin (22/10/18 09:05 AM IDT)
Paul Shaw (24/10/18 07:39 AM IDT)
Andrea Andenna (24/10/18 09:49 PM IDT)
Mykola Zubach (26/10/18 01:05 PM IDT)
Mingliang Zeng (29/10/18 05:51 AM IDT)
Tyler Mullen (30/10/18 09:07 PM IDT)
David Greer (01/11/18 03:14 AM IDT)
Li Li (01/11/18 04:45 AM IDT)