1. Two-headed and seven-headed dragons came to a meeting. At the very beginning of the meeting, one of the heads of one of the seven-headed dragons counted all the other heads. There were 25 of them. How many dragons in total came to the meeting?
Answer: 8 dragons. Solution. Subtract the 6 heads belonging to the seven-headed dragon from the 25 heads counted by the seven-headed dragon. 19 heads remain. The remaining dragons cannot all be two-headed (19 is an odd number). There can only be one more seven-headed dragon (if there were two, an odd number of heads would remain for the two-headed dragons. And for three seven-headed dragons, there would not be enough heads ($7 \cdot 3=21>19$)). Subtract the 7 heads of this single dragon from the 19 heads, and we get the total number of heads belonging to the two-headed dragons. Therefore, the number of two-headed dragons: (19 - 7) $: 2=6$. In total: $6+1+1=8$ dragons.

Grading criteria: Full solution - $\mathbf{7}$ points. Only answer - $\mathbf{2}$ points.