do this !!!

a pile of n pebbles is placed in a vertical coloumn. this configuration is modified according to the following rules. a pebble can be moved if it is at the top of the coloumn which contains atleast 2 more pebbles than the coloumn immediately to its right.(if there are pebbles to right, think of this a s a coloumn with 0 pebbles). at each stage choose a pebble from among those that can be moved (if there are any) and place it at the top of the coloumn to its right. if no pebbles can be moved , the configuration is called a final configuration. for each n, show that no matter what choices are made at each stage, the final configuration obtained is unique. describe that configuration in terms of `n`.

source : titu