$\underline{\text { Folklore }}$

A village is built in the form of a 3 by 3 square grid of blocks (blocks are squares with side $b$, making a total of 9 blocks). What is the shortest path that an asphalt paver must travel to pave all the streets, if it starts and ends its journey at the corner point $A$? (The sides of the square are also streets).

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There are 24 segments (streets) of length $b$ that the asphalt paver must drive on. Eight intersections have an odd number of such segments. The asphalt paver will have to drive one of these segments, which leads to such an intersection, twice. Since a segment connects two intersections, there are no fewer than $8 / 2 = 4$ extra drives. Therefore, the total distance will be no less than $24 b + 4 b = 28 b$.

The example in the figure shows that a path of this length is possible.

![](https://cdn.mathpix.com/cropped/2024_05_06_73983c7cc26f0024f238g-02.jpg?height=592&width=583&top_left_y=1648&top_left_x=746)

## Answer

$28 b$.

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