Puzzle
2 minute read

Ponder This Challenge - October 2018 - Different area triangles

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

Solution

  • Oleg Vlasii was the first to send us the smallest square solution: 24x24
    [[20,0], [0,1], [3,13], [7,18], [6,2], [23,22], [4,23], [24,9], [19,24], [12,2], [23,7]]

    Alper Halbutogullari sent us the most elongated: 66x9
    [[11,0],[66,1],[0,2],[53,3],[5,4],[65,5],[63,6],[1,7],[18,8],[8,9],[66,9]]

    and we received the solution with the smallest area (528) from Hermann Jurksch: 33x16
    [[0,12],[1,6],[2,1],[4,15],[6,2],[17,3],[23,16],[27,16],[32,0],[32,14],[33,5]]

Solvers

  • 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)
  • 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)

Related posts