8.1. In a circle, 58 balls of two colors - red and blue - are arranged. It is known that the number of triples of consecutive balls, among which there are more red ones, is the same as the number of triples with a majority of blue ones. What is the smallest number of red balls that could be present?

![](https://cdn.mathpix.com/cropped/2024_05_06_6c94238ddc8917ebef5dg-8.jpg?height=891&width=897&top_left_y=231&top_left_x=591)
Answer: 20

Evaluation

There are a total of 58 threes, so the number of threes with dominance of each of the two colors is 29. Therefore, the number of red balls should be no less than $\frac{2}{3} * 29$, which is no less than 20.

Example

![](https://cdn.mathpix.com/cropped/2024_05_06_6c94238ddc8917ebef5dg-8.jpg?height=888&width=893&top_left_y=1418&top_left_x=570)