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Checklist VsOSh AI 2026 Regional Stage, Tour 1 (mathematics) · C task

Mean and Median

Russian title: Среднее и медиана

Find the largest possible gap between the mean and the median of ten points under spacing and coverage constraints.

  • Optimisation (order statistics)
  • Russian original · English translation
Download the English statement Open the task PDF (Russian)

The task

Let x₁, …, x₁₀ ∈ [0, 1] with |x_i − x_j| ≥ 0.01 for all i ≠ j, and suppose every subinterval [a, a + 0.25] ⊂ [0, 1] contains at least one of the points.

With x̄ the mean and m = (x₍₅₎ + x₍₆₎)/2 the median, find the maximum of |x̄ − m|.

Abridged and translated by SOTA from the official Russian materials. The official statement has the exact rules, and it wins wherever this summary differs.

In English

This task was published in Russian. SOTA translated its 3 files into English on 16 September 2026. Only the words changed in the notebooks: markdown, code comments, messages and printed output. The code, file names and paths are the original's, so a translated notebook runs with the original data.

Read the task statement in English 238 words

Mean and Median

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

All-Russian School Olympiad in Informatics 2025–2026, Regional Stage, Grades 9–11
“Artificial Intelligence” profile, Tour 1, 17 January 2026
Task C

Points for the task: 50
Answer submission format: entering the answer
Number of attempts: 10
Submission that counts: the last one

Statement

Let x1,…,x10∈[0,1]x_1, \dots, x_{10} \in [0, 1], and let the following conditions hold:

∣xi−xj∣≥0.01for all i≠j,|x_i - x_j| \ge 0.01 \quad \text{for all } i \ne j,

and every subsegment [a,a+0.25]⊂[0,1][a, a + 0.25] \subset [0, 1] contains at least one point of the set {x1,…,x10}\{x_1, \dots, x_{10}\}.

Sort the numbers:

x(1)≤x(2)≤⋯≤x(10).x_{(1)} \le x_{(2)} \le \dots \le x_{(10)}.

Denote by

x‾=110∑k=110x(k),m=x(5)+x(6)2\overline{x} = \frac{1}{10} \sum_{k=1}^{10} x_{(k)}, \qquad m = \frac{x_{(5)} + x_{(6)}}{2}

the mean and the median (taken as the mean of the two middle numbers in order).

By how much at most can the mean x‾\overline{x} differ from the median mm? That is, find

max⁡∣x‾−m∣\max |\overline{x} - m|

under the conditions described.

Output format

Round the answer to 6 decimal places, using a point as the decimal separator.

Scoring

An exact match of the answer: 50 points.

Test results are not available during the tour.

Translated by SOTA. The Russian original is the official version and wins wherever the two differ. The statement is translated from the tour's PDF paper; the official editorial is a single notebook covering all tasks of the tour. If you organise this olympiad and would like the translation removed, email [email protected] and we will take it down.

At a glance

You get
Statement only.
You submit
A number rounded to 6 decimal places (decimal point).
Scoring
Answer entry; 50 points for an exact match; 10 attempts, the last one counts; results hidden during the tour.
Rules
  • Python may be used, or the problem may be solved purely mathematically.
Format
Regional stage, Tour 1, 17 January 2026; grades 9–11; individual; 300-minute tour (Moscow procedure); answers entered in Yandex Contest.

In English (SOTA)

Statement

Solutions

Results

Source files

Details

Year
2026, Regional venues across Russia (in person)
Round
Regional Stage, Tour 1 (mathematics) · C task
Language
Russian; English translation by SOTA
License
Not stated by the source