8-4. In a giraffe beauty contest, two giraffes, Tall and Spotted, made it to the final. 105 voters are divided into 5 districts, each district is divided into 7 precincts, and each precinct has 3 voters. The majority of voters on each precinct choose the winner of their precinct; in a district, the giraffe that wins the majority of precincts wins the district; finally, the giraffe that wins the majority of districts is declared the winner of the final. The giraffe Tall won. What is the minimum number of voters who could have voted for him?
Answer: 24.

Solution. For High to win the final, he must win in 3 districts. To win a district, High must win in 4 precincts of that district. In total, he needs to win in at least $3 \cdot 4=12$ precincts. To win in a precinct, at least 2 voters must vote for him. Therefore, at least 24 voters are needed.

Comment. In problems with questions like "what is the greatest" and "what is the least," the solution usually consists of two parts: estimation and example. Estimation is the proof that a greater (or lesser, depending on the question) answer cannot be achieved, and the example is the proof that the given answer can be achieved.

In the solution above, we did not provide an example (i.e., did not prove) that 24 voters are sufficient. For completeness, the solution is missing the phrase: "From the above reasoning, it is clear that 24 voters for High can be sufficient: 2 voters per 4 precincts in any 3 districts."