[psyang]

Originally Posted by GGG

I don’t think that is different than MG saying the Max distance between any two adjacent coins is 1/root2

I think there is a difference.

Spoiler!

In the solution, it only considers the minimum distance to not cause an overlap, which is 2 (centre-centre distance). To me, this is more precise because it doesn't matter what the coins arrangements are - this distance will always hold. An empty space in the radius 2 covering is all areas that are at least 1 unit away from *any* coin edge, which means a coin must be able to be placed there.

MG tried to find the maximum distance between coins, which is less obvious. If two coins are 2sqrt(2) apart (centre-centre distance), is it clear that a coin can fit between them? It might be the case, but it's not obvious - other coins may come into play preventing a coin from being placed.

Maybe I'm misinerpreting what MG is saying - if so, please someone put up a diagram to make it more clear.