8Everything else is stable! InstabilityEverything else is stable!
9ImplicationsTop most level, or the level just below it, is always full.The tower is stable, unless it contains the forbidden level:Two towers that differ only in the order of the levels are equivalent!
33Stability and linear programming A tower is weakly stable if and only if its corresponding linear program is feasible.A tower is stable if and only if its corresponding linear has a strictly positive feasible point.
34Simple Variations of JENGA Remove a block from anywhere and put it anywhere on the top level. If the top level is full, then start a new level.Remove a block from anywhere and put it anywhere on top, or start a new level. If a block from the top level is removed, then it must start a new level.
35More complicated variations of JENGA Remove a block from anywhere, and put it anywhere higher. (Filling in gaps is allowed.)Remove a block, or slide it outward by a multiple of 1/k of the length of a block. If a block is completely removed, then put it anywhere on top.
36Free Play JENGAkRemove a block from anywhere, and put it in an arbitrary position at the top level, or start a new level, not necessarily in one of the fixed k positions of standard JENGAk games.
37More basic open problems Which positions in JENGAk are:REACHABLE?CONSTRUCTIBLE?SCULPTUREABLE?