## 4. task

Antun and Branko participated in a race. All runners finished the race, and no two runners finished at the same time. The number of runners who finished the race before Antun is half the number of runners who finished after him. The number of runners who finished the race before Branko is equal to the number of runners who finished after him. Exactly 15 runners finished the race after Antun but before Branko. How many runners participated in the race?
## First Method

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

................................................................................

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_6273b59ad7665824c90fg-5.jpg?height=68&width=1620&top_left_y=1071&top_left_x=138)

According to the condition of the problem, we have:

$\ldots \ldots \ldots . .=15$

$\ldots \ldots \ldots \ldots .=15+1=16$

.......................................................... 32

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