We will simplify the game to 4 critical positions per ring: up, down, left and right. Four actions, with the same names mean we tip the puzzle in that direction and hold it until all balls come to rest. Ignore ball collisions. Balls roll along the rings, resting when they either balance stably on top of a "hill" or at the bottom of a "cup". Balls pass through any "gap" they touch at any point in their path if the current action is aligned with the gap. Examples: 1. One ball starting at 2U passes the gap with action down, resting on the hill at 1U. After left it rolls into the cup at 1L. Finally, after down it ends at 1D. 2. One ball starting at 4R, passes the gap with action left, resting at 3R. After down it roll