B3. We start with a square with side 1. In the first minute, squares with side $\frac{1}{3}$ grow in the middle of the vertical sides. In the next minute, squares with sides of $\frac{1}{3}$ of the length of those line segments grow in the middle of all vertical line segments of the new figure. See below for the situation after 0, 1, and 2 minutes.
![](https://cdn.mathpix.com/cropped/2024_04_17_fd6be77049c724ba1866g-1.jpg?height=178&width=880&top_left_y=1966&top_left_x=586)

This process continues. Every minute, a square with a side of $\frac{1}{3}$ of the length of each vertical line segment grows in the middle of each vertical line segment. After an hour, squares have grown 60 times.

What is the perimeter of the figure after an hour?
B3. 84

The perimeter of the figure consists of horizontal and vertical line segments. When a square is added, a vertical line segment is split, and the middle part of it shifts to the side, while the total length of the vertical line segments remains the same. Therefore, we only need to look at how many additional horizontal line segments are added; in the figure below, these new segments are colored red.
![](https://cdn.mathpix.com/cropped/2024_04_17_123a6e1baa7323ff717cg-1.jpg?height=168&width=874&top_left_y=2666&top_left_x=590)

In the first minute, four segments of length \(\frac{1}{3}\) are added, which is a total of \(\frac{4}{3}\). In the second minute, twelve segments of length \(\frac{1}{9}\) are added, which is also a total of \(\frac{4}{3}\).

Each minute, each vertical line segment is split into three, causing three times as many squares to grow in each subsequent minute. Thus, in each minute, three times as many segments are added compared to the previous minute, but they are also \(\frac{1}{3}\) the length of the previous segments. We conclude that \(\frac{4}{3}\) is added to the perimeter of the figure each minute. After 60 minutes, the perimeter is therefore \(4 + 60 \cdot \frac{4}{3} = 84\).