Problem 4.5. Hooligan Dima made a construction in the shape of a $3 \times 5$ rectangle using 38 wooden toothpicks. Then he simultaneously set fire to two adjacent corners of this rectangle, marked in the figure.

It is known that one toothpick burns for 10 seconds. How many seconds will it take for the entire construction to burn?

(Fire spreads along the toothpicks at a constant speed. The fire continues to spread from each burned toothpick to all adjacent unburned toothpicks.)

![](https://cdn.mathpix.com/cropped/2024_05_06_3890a5f9667fd1ab5160g-04.jpg?height=458&width=359&top_left_y=110&top_left_x=547)
Answer: 65.

Solution. In the picture below, for each "node", the point where the toothpicks connect, the time in seconds it takes for the fire to reach it is indicated. It will take the fire another 5 seconds to reach the middle of the middle toothpick in the top horizontal row (marked in the picture).

![](https://cdn.mathpix.com/cropped/2024_05_06_3890a5f9667fd1ab5160g-04.jpg?height=464&width=357&top_left_y=826&top_left_x=548)