Problem - 3834
There are three piles which contain $8$, $9$, and $19$ stones, respectively. You are allowed to choose two piles and transfer one stone from each of them to the third pile. Is it possible to make all piles all contain exactly $12$ stones after several such operations?
No. Consider $\pmod{3}$ of the numbers of stones in each pile. They will always equal to $0$, $1$, and $2$, initially and after each operation.