Consider a 2 x 2 x height stack of cube-shaped boxes of identical size. The stack has height levels of boxes, each level containing 4 boxes arranged in a 2 x 2 pattern. Each box has a 50% probability of containing dynamite and a 50% probability of being empty. Two dynamite-filled boxes, A and B, are in the same dynamite cluster if:
A stack is dangerous if it contains a dynamite cluster that contains at least dangerousClusterSize boxes. Given height and dangerousClusterSize, compute the probability that the stack is dangerous.
- a face of A touches a face of B
- OR a face of A touches a face of some box C, and C is in the same dynamite cluster as B.