There are 7 lines in the plane. A point is called a [i]good[/i] point if it is contained on at least three of these seven lines. What is the maximum number of [i]good[/i] points?
1. **Counting Intersections:**
   - There are 7 lines in the plane. The maximum number of intersections of these lines can be calculated by choosing 2 lines out of 7 to intersect. This is given by the binomial coefficient:
     \[
     \binom{7}{2} = \frac{7 \times 6}{2 \times 1} = 21
     \]
   - Therefore, there are at most 21 intersection points. However, a point is called a *good* point if it is contained on at least three of these seven lines.

2. **Counting Good Points:**
   - For a point to be a *good* point, it must be the intersection of at least three lines. We need to determine the maximum number of such points.
   - Consider the dual problem: we are looking for 7 points such that each line goes through at least three points. This is equivalent to finding a configuration where each line intersects at least three other lines.

3. **Configuration Analysis:**
   - Consider the standard configuration of 7 points in the plane such that each line through any three points intersects at least three other lines. This is known as a Ceva configuration.
   - In a Ceva configuration, the points are arranged such that each line intersects exactly three points. This configuration can be visualized using the concept of barycentric coordinates and the properties of triangles.

4. **Maximal Triangle Argument:**
   - Choose the maximal triangle by area formed by three points, say $\triangle ABC$. If there are points outside this triangle, say $P$, we analyze the position of $P$ relative to $\triangle ABC$.
   - If $P$ has barycentric coordinates such that it lies outside $\triangle ABC$, then we can find a point $Q$ such that the new triangle $\triangle ABQ$ or $\triangle ABP$ is larger than $\triangle ABC$. This contradicts the assumption that $\triangle ABC$ is maximal.
   - Therefore, all points must lie within $\triangle ABC$. This implies that the configuration must be a Ceva configuration, where three points lie on the segments of the triangle and one point lies in the interior.

5. **Ceva Configuration and Menelaus' Theorem:**
   - In a Ceva configuration, the three points on the segments must be collinear. However, this is impossible due to the extra condition imposed by Menelaus' theorem, which states that for three points on the sides of a triangle to be collinear, a specific ratio condition must be satisfied.
   - Since this condition cannot be met, it implies that having 7 good points is impossible.

6. **Conclusion:**
   - The maximum number of good points is 6, as having 7 good points leads to a contradiction.

The final answer is $\boxed{6}$.