Question 83
There are $2009$ pebbles in some points $(x, y)$ with both coordinates integer. An operation consists in choosing a point $(a, b)$ with four or more pebbles, removing four pebbles from $(a, b)$ and putting one pebble in each of the points
$$
(a, b - 1), (a, b + 1), (a - 1, b), (a + 1, b)
$$
Show that after a finite number of operations each point will necessarily have at most three pebbles. Prove that the final configuration doesn't depend on the order of the operations.
$$
(a, b - 1), (a, b + 1), (a - 1, b), (a + 1, b)
$$
Show that after a finite number of operations each point will necessarily have at most three pebbles. Prove that the final configuration doesn't depend on the order of the operations.