On the Island of Misfortune with a population of 96 people, the government decided to carry out five reforms. Each reform is opposed by exactly half of all citizens. A citizen will go to a rally if they are dissatisfied with more than half of all the reforms. What is the maximum number of people the government can expect at the rally?
Let $x$ be the number of people who came out to the rally. Consider the total number of "dissatisfactions." On one hand, each reform is opposed by exactly 48 residents, so the total number of dissatisfactions is $48 \cdot 5 = 240$. On the other hand, each person who came out to the rally is dissatisfied with at least three reforms. Therefore, the total number of dissatisfactions is no less than $3x$. Thus, $240 \geq 3x$, from which $x \leq 80$.

Let's provide an example where exactly 80 people come out to the square. Choose 80 people among the residents and divide them into five groups of 16 people each (the remaining 16 people form the government). Let the first reform be opposed by people from the first three groups, the second reform by people from the second, third, and fourth groups, the third reform by people from the third, fourth, and fifth groups, the fourth reform by people from the fourth, fifth, and first groups, and the fifth reform by people from the fifth, first, and second groups. Then, each reform is opposed by exactly $3 \cdot 16 = 48$ people, and the chosen 80 people will come out to the rally.

## Answer

80 people.