7.14 There is a $5 \times 5$ square grid chessboard, consisting of 25 $1 \times 1$ unit square cells. At the center of each unit square cell, a red dot is painted. Please find several straight lines on the chessboard that do not pass through any red dots, dividing the chessboard into several pieces (which may be of different shapes and sizes), such that each piece contains at most one red dot. How many straight lines do you need to draw at a minimum? Provide an example of such a drawing and prove your conclusion.
[Solution] As shown in the figure, after dividing the chessboard into several sections with 8 straight lines, there is at least one red point in each small section.

Below, we use proof by contradiction to show that it is impossible to have fewer lines that satisfy the requirements of the problem.

Assume that the number of lines drawn does not exceed 7, and they meet the requirements of the problem.

At this point, we connect the 16 red points on the edge sequentially with unit-length line segments to form a square with a side length of 4. Since the 7 lines drawn intersect at most 14 of these small line segments, at least two unit-length small line segments do not intersect with any of these 7 lines, and they must entirely fall into one of the small regions divided by these lines, including their two endpoints (red points), which contradicts the problem's requirements.
Therefore, at least 8 lines are needed.