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?