Combinatorial rule for a stable stack of bricks.

Solution 1:

Although probably not a combinatorial rule per se, here is an algorithm that could be used to find unstable equilibria or configurations that would not be in equilibria:

1) Identify all bricks with only 1 supporting brick.

2) For each of these bricks consider the bricks above it connected to it by an upward facing V. (These are the only bricks that put any weight onto the brick, and therefore determine its stability.)

3) If this group of bricks has a center of gravity that is directly over the supporting brick, then the configuration is stable. If the center of gravity is directly over the edge of the supporting brick then it is unstable. If the center of gravity is over the unsupported side then it is not in equilibrium and will fall due to gravity.

4) If all singly supported bricks are in stable equilibrium, then the entire configuration is also. Else, if all singly supported bricks are either stable or unstable, then the configuration is unstable. Else, the configuration is not in an equilibrium.