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

AI Thread Summary
The discussion centers on arranging n points within a square of side length a while ensuring that the distance between any two points is at least 1. Participants explore methods to generate random points while maintaining this minimum distance, highlighting the challenge of ensuring point-to-point separation. The conversation also touches on the possibility of using a grid system to guarantee the required distance and questions whether there are specific values of a that would make the arrangement impossible. Overall, the problem is presented as an open question, inviting creative solutions and critical thinking. The exploration of this geometric arrangement presents both mathematical and practical implications.
Galizius
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Please post this type of questions in the homework forums, and always show how you tried to solve the problem by yourself.
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.
 
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And we would like to see your thoughts on the problem.
 
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.
 
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?
 
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