12. The Zmey Gorynych has 2000 heads. A legendary hero can cut off 33, 21, 17, or 1 head with one strike of his sword, but in return, the Zmey grows 48, 0, 14, or 349 heads respectively. If all heads are cut off, no new ones grow. Can the hero defeat the Zmey? How should he act?
12. $2000=94 \cdot 21+26$. This means that after cutting off 21 heads 94 times, 26 heads will remain. We notice that if 17 heads are cut off, 14 will grow back, i.e., the number of heads will decrease by 3. Then, we perform this three times, and $26-3 \cdot 3=$ $=17$ will remain, which can be cut off with the final blow.