IBM Ponder This #246 · October 2018

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.

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

Solution

Best opened after a real attempt

To be added.