9 Dec
2010
9 Dec
'10
12:56 p.m.
What is the minimum number of points that cannot be covered by unit diameter coins? This is from Naoki Inaba ( http://www.janko.at/Raetsel/Naoki/ ) A fuller explanation: Coins (of a unit diameter) can be packed in a square or hexagonal lattice. Either packing has holes. http://mathworld.wolfram.com/CirclePacking.html If there were 3 points on the plane, the coins could be moved to cover the points. If there were 3 million points on the plane, about 10% of them would be in the holes. (Packing density is pi sqrt(3)/6) Problem -- What is the minimum number of points that cannot be covered by coins? --Ed Pegg Jr