Problem 2. Duorites are creatures that have two horns, while heptorites have 7 horns. In one herd, there were both types of creatures. Together, they had 16 horns. How many duorites and heptorites were there in this herd?
Solution. If the herd consists of 8 duors, then they would have $8 \cdot 2=16$ horns, which is not possible since according to the condition, there is at least one heptor in the herd. Therefore, the number of duors in it is less than or equal to 7. The total number of duors cannot be equal to or greater than 5, because $16-2 \cdot 5=6$, and according to the condition, the heptor has 7 horns. Thus, the number of duors in the herd can be $1, 2, 3$ or 4. By sequential verification, it is found that this herd has exactly 1 duor and two heptors.