Problem 1. On the surface of a planet shaped like a donut, two snails crawled, leaving trails behind: one along the outer equator, and the other along a spiral line (see figure). Into how many parts did the snails' trails divide the surface of the planet? (It is sufficient to write the answer.)

![](https://cdn.mathpix.com/cropped/2024_05_06_451a0d7107599630d1d3g-09.jpg?height=249&width=422&top_left_y=469&top_left_x=516)

## [4 points] (S.K. Smirnov, I.V. Yashchenko)
Answer: 3.

Comment. Let's imagine the surface of a donut made of paper. Cut it along the path of the first snail and unfold it. We will get the lateral surface of a cylinder. The path of the second snail will be cut in three places. That is, on the resulting surface, the trail of the second snail represents three lines connecting the bottom base of the cylinder with the top. It is not difficult to realize that they divide the lateral surface of the cylinder into 3 parts.

![](https://cdn.mathpix.com/cropped/2024_05_06_451a0d7107599630d1d3g-09.jpg?height=345&width=297&top_left_y=881&top_left_x=978)