How Can You Arrange Points in a Square While Maintaining a Minimum Distance?

[Galizius]

I am wondering how can I solve following problem.

Arrange randomly n points inside a square of the side length a under the condition that the distance between any two points may not be smaller than 1.

I would like to see how can it be solved.

 

[Borek]

And we would like to see your thoughts on the problem.

 

[Galizius]

I was trying to make n random numbers in the selected a side length but I do not know how to make sure that the point-to-point distance between every of the n points will be always bigger than 1.

 

[Borek]

I believe this is an open question - that is, you are expected to show you can think, and there is one correct solution.

Can you think of any grid of (not random) points, where the shortest distance is guaranteed to be 1?

Can you think of an a for which there is no solution?