Plots Above the Median

Plots Above the Median

English translation by SOTA – AI Community of the Russian original. Organisers who would like this translation removed can email [email protected].

Task 6 of the school stage of the All-Russian School Olympiad (VsOSh) 2025/26 in artificial intelligence (region group I), grades 9–11. The official answer and solution are in a separate file.

Botanists are planning a field experiment. In a preliminary study, they selected several plots and on each of them counted the trees of two species:

$$x_1 \text{ — the number of maples}, \qquad x_2 \text{ — the number of lime trees}.$$

In addition, the botanists recorded their opinion on whether each plot is suitable for the experiment:

$$y = \begin{cases} 1, & \text{if the plot is suitable;} \\ 0, & \text{if it is not suitable.} \end{cases}$$

The director of the nature reserve assessed the plots by his own criterion:

$$s = 0.4 \cdot x_1 + 0.6 \cdot x_2.$$

He computed the median of all the values of $s$ (let us denote it Median) and allowed the experiment to be carried out only on the plots that simultaneously satisfy the conditions:

$$y = 1 \quad \text{and} \quad s \ge \text{Median}.$$

Problem. How many plots satisfy these conditions?

Explanation. The median Median is a value that divides an ordered set of numbers into two parts of equal size. If the number of elements is even, the median is taken to be the arithmetic mean of the two central values.

Data. The table is in a separate file (in XLSX, ODS or CSV format), where each row contains the values $x_1$, $x_2$ and $y$ for one plot.

Scoring criterion: exact match of the answer — 12 points

Maximum score for the task — 12