6. In a school quiz, 100 students participated. After the results were tallied, it turned out that any 66 of them together earned no less than $50 \%$ of the total prize points. What is the highest percentage of points that one participant could have earned?
Answer: $25 \%$.

Solution: Suppose participant $\mathrm{X}$ scored the highest percentage of points $-x \%$. Divide the remaining participants into three groups A, B, and C, each with 33 people. Let the total percentages of points scored by these groups be $a, b$, and $c$ respectively. Then,

$$
2(100-x)=2(a+b+c)=(a+b)+(a+c)+(b+c) \geq 50+50+50=150.
$$

Therefore, $x \leq 25$.

Let's provide an example where the maximum percentage is 25. If each participant, except for $\mathrm{X}$, earned $\frac{75}{99}=\frac{25}{33} \%$ of all points, then any 66 of them would collectively score $50 \%$, while $\mathrm{X}$ would score $25 \%$ of all points.

Grading criteria: Correct and justified solution - 7 points, only the estimate "not more than $25 \%$ " is proven - $\mathbf{4}$ points, only a suitable example is provided - $\mathbf{3}$ points, the solution is incorrect or only the answer is given - $\mathbf{0}$ points.