Spinoff from another thread, on,*inter alia*, outlines of US shapes: http://boards.straightdope.com/sdmb/showthread.php?t=767136

I found this:

Which prompted the pleasant response:

Puzzle enthusiasts and mathematicians study this type of stuff, and come up with classes of and maximum tilings all the time. Given the outline of the continental United States (CONUS), how many ways could the outlines of the states (handy separated list here: http://m.imgur.com/KfIhxkf?r) be apportioned to fit into it, given certain leeway?

How do you even approach the problem?

That “leeway” and how to come up with it–and approximating/classifying conditions is what I’m hoping to learn about. For example, the multiple sub tilings of the four-corner trapezoids (ok, one with a jigger)–can that be subsumed as part of the general analysis?