There are three virtual piles of stones. In one operation one may add to, or remove from, one of the piles the number of stones equivalent to the quantity in the other two piles combined, leaving the numbers in those two piles unchanged.
Thus, e.g., (12,3,5) can become (12,20,5) by adding 12+5=17 stones to the second pile, or (12,3,5) can become (4,3,5) by removing 3+5=8 stones from the first pile.

Assume a starting state (1111,111,11).
Is it possible, by a sequence of such operations, reach a state where one of the piles is empty?