One, (20 points) A class participated in an intelligence competition, with three questions: $a$, $b$, and $c$. Each question either scores full marks or 0 points, where question $a$ is worth 20 points, and questions $b$ and $c$ are each worth 25 points. The competition results show that each student got at least one question correct, one person got all three questions correct, and 15 people got two questions correct. The number of students who got question $a$ correct plus the number of students who got question $b$ correct is 29; the number of students who got question $a$ correct plus the number of students who got question $c$ correct is 25; the number of students who got question $b$ correct plus the number of students who got question $c$ correct is 20. What is the average score of the class?
Let $x_{a}, x_{b}, x_{c}$ respectively represent the number of people who answered questions $a$, $b$, and $c$ correctly, then we have
$$
\begin{array}{l}
\left\{\begin{array}{l}
x_{a}+x_{b}=29, \\
x_{a}+x_{c}=25, \\
x_{b}+x_{c}=20 .
\end{array}\right. \\
\therefore x_{a}+x_{b}+x_{c}=37 .
\end{array}
$$

Solving, we get $x_{a}=17, x_{b}=12, x_{c}=8$.
The number of people who answered 1 question correctly is $37-1 \times 3-2 \times 15=4$.
The total number of students in the class is $1+4+15=20$.

Answer: The average score of the class is 42 points.