5. The Zmey Gorynych has 2000 heads. A legendary hero can cut off $1, 17, 21$ or 33 heads with one blow, but in return, $10, 14, 0$ or 48 heads grow back, respectively. If all heads are cut off, no new ones grow. Can the hero defeat the Zmey?
5. We can propose the following tactic for cutting off the heads of the Snake: 1. Initially, we will cut off 21 heads (94 times); no new heads will grow, and the Snake will be left with 26 heads. 2. Next, we will cut off 17 heads three times (remember, 14 new heads will grow back each time) - after which 17 heads will remain to be cut off. 3. With the final blow, we will cut off the remaining 17 heads.