Task 1. The administration divided the region into several districts based on the principle: the population of a large district exceeds $8 \%$ of the region's population and for any large district, there are two non-large districts with a combined population that is larger. Into what minimum number of districts was the region divided?
Answer: 8 districts.

Solution. The number of "small" districts is no less than 2 according to the condition, and their population does not exceed $8 \%$ of the total population of the region. We will show that the number of districts in the region is no less than 8. If the number of districts in the region is no more than 7, but there are no more than 5 "large" districts with a population of less than $16 \%$ each. Then the total population of the region cannot amount to $100 \%$. Indeed, $2 \cdot 8 \%+5 \cdot 16 \%=96 \%<100 \%$. Thus, the number of districts in the region is no less than 8. A division into 8 districts is possible, for example, $8 \%+8 \%+14 \%+14 \%+14 \%+14 \%+14 \%+14 \%=100 \%$.