[GGG]

Originally Posted by psyang

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.

I think that’s it’s clear that if there is not a 1/root2 space between adjacent horizontal coins and a diameter diagonal space between diagonal coins.

The expansion to radius 2 of a coin effectively adds a diagonal space of a diameter which is what the root2 spacing is stating.