While playing a city builder game, I noticed that the area of the buildings I can place on the game map is lower than the area of the map itself, since I need to place the roads that connect all buildings to a central block, and they occupy space themselves.
That brings the question: Is it possible to predict, for a certain group of rectangles, if it's possible to tile a given finite plane while keeping the rule that every rectangle has a point in their perimeter that can trace an unobstructed path to an arbitrary point?
I have played around for an afternoon, but came up blank. One can easily eliminate any group that contains a total area larger than the plane, or an individual rectangle with a dimension larger than the plane's, but I have not been able to think of a general solution.