Math Is Fun Forum

Hi friends,

I've this kind of problems.
Supposing to have a cube volume in the (x,y,z) space with width equal to 1. Supposing also 10 points uniform division of each width along x,y,z respectively. By crossing the three points divisions this means that the cube contains 10x10x10=1000 points (I hope ).

Given an arbitrary number N, among these 1000 points i must guess the N points which cover the volume in an "uniform" way which means, for instance:
- if N=1, i must guess the central point
- if N=2, ... 2 edges
- if N=3, ... 2 edges an the central point
- if N=4, ... 4 edges
- if N=5, ... 4 edges + central point
- and so on

If I correctly remember this should be related to some "maximum entropy" fundaments.
Does anyone know how can I develop a basic algorithm to implemet this procedure?
Considering also that I aim to deal with space with arbitrary dimension.
Thanks and regards.
Claudio