[psyang]

Originally Posted by bizaro86

This is a good question, imo.

I misread it initially, and my solution assumed the coins were touching each other, which wasn't stated in the problem.

In many ways this reminds me of a reservoir engineering problem. The spaces in between the coins would be porosity (just 2d instead of 3d). Having the coins not touching would make it a non-physical solution, but you'd have perfectly sorted matrix with exactly equal grain sizes.

I think the answer probably flows from your observation about the distance between the coins. I don't see the solution but have the following observations.

The number of coins given is 400, or 4:1 for the number of initial coins. That ratio isn't physical, but 4 is 2 squared, and we know the distance between the centers of the coins can't be bigger than 2D, because then you could fit another coin.

I think the proof will involve squaring that distance and demonstrating that 4x is enough coins to cover it somehow.

I didn't spoiler this because its just middle of the night musings, and could be completely unhelpful to anyone...

This is the type of discussion I wanted this thread to encourage. I hope others add their thoughts too!