## 2. task

Fran and Leon participated in a race. All runners finished the race, and no two finished at the same time. The number of runners who finished the race before Fran is equal to the number of runners who finished after him. The number of runners who finished the race before Leon is half the number of runners who finished after him. Exactly 15 runners finished the race between them. How many runners participated in the race?
First method

Notice that Fran finished the race in the middle, and Leon has more runners behind him than in front of him, so Leon finished the race ahead of Fran. Let's mark Leon's (A) and Fran's (B) positions on the diagram.

![](https://cdn.mathpix.com/cropped/2024_05_30_22f201ffe2378dbba52dg-2.jpg?height=152&width=594&top_left_y=1483&top_left_x=731)

The colored blocks in each row are equal.

Therefore, on the next image, the gray block is one less than the yellow block:

![](https://cdn.mathpix.com/cropped/2024_05_30_22f201ffe2378dbba52dg-2.jpg?height=60&width=592&top_left_y=1940&top_left_x=732)

According to the condition of the problem, we have:

$$
\begin{aligned}
& \ldots . \ldots \ldots . .=15 \\
& \ldots . . . . . . .=15+1=16 \\
& \ldots . . . . . . . . . . . . . . . . . . . . . . B . . . . . . . . . .=15+1+16=32
\end{aligned}
$$

In total, there were $3 \cdot 32+1=97$ runners.