The point is, you don't need to mesh lots of points for each solid, unless you want to make it flexible. The only boundary conditions would be at the joints between rigid bodies, and always less than six at each.
For example if that 2D human body in the game Tulac posted had say 13 joints, each with one DOF allowed (angle) and two restricted ones (position in 2D), that would mean 13x2=26 boundary conditions. These conditions are trivial equations, actually after applying them you have the same system but with 26 variables less, that is a simpler system (than if you had to account for each body part moving free).
OK back to topic, this is silly:
http://freeonlinegames.com/puzzle-ga...-go-happy.html