Consider a with 3 × 3 grid where each cell contains a number of coins; for example, the following represents a possible configuration of coins on the grid (the integer in each cell is the number of coins in that cell):12 3 11 8 42 13 0This configuration is transformed in stages as follows: in each step, every cell sends a coin to all of its neighbors (horizontally or vertically, not diagonally), but if there aren’t enough coins in a cell to send one to each of its neighbors, it sends no coins at all. For example, the above would result in the following after one step:11 2 34 7 21 12 2a) Show that every staring configuration results in stable configuration (one that no longer changes in this process), or repeatedly cycles through ???? configurations for some positive integer ???? (i.e., those same ???? configurations appear repeatedly in the sequence over and over as the transformation is applied).b) In the case that the initial configuration eventually cycles through ???? configurations, what are the possible values of ?????c) Either prove that for some positive integer ????, every configuration will reach a stable configuration or a repetition of a ????-cycle in ???? or fewer steps, or prove there is no such B.
