Checklist VsOSh AI 2026 Final Stage, Tour 1 (theory) · B task
Random Generator
Russian title: Генератор случайности
Find the parameter m that maximises the likelihood of an observed, partially masked sequence of uniform random numbers.
The task
Given a natural number m ≥ 6, a generator outputs 10 numbers, each chosen independently and uniformly from {1, 2, …, m}. Because of a bug, the numbers 1–5 are displayed unchanged, while any other number is displayed as 6.
For which natural m ≥ 6 is the probability of seeing the sequence 6, 2, 6, 6, 1, 6, 4, 6, 3, 5 on the screen maximal?
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 4 files into English on 17 September 2026.
- Task statement Russian original of Task statement
- Official solution Russian original of Official solution
- Full paper (all tasks of the tour) Russian original of Full paper (all tasks of the tour)
- All solutions of the tour with marking criteria Russian original of All solutions of the tour with marking criteria
Read the task statement in English
Random Generator
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, Final Stage
“Artificial Intelligence” profile, Tour 1, Moscow, 23 March 2026
Task B
A random number generator works as follows. If it is given a natural number , it outputs 10 natural numbers one after another. Each number is chosen by it independently and with equal probability from the set .
Because of a system error, the generator's result is displayed on the screen as follows: the numbers are displayed unchanged, and in place of any other number the number is displayed.
For which natural number is the probability of getting the sequence of numbers
on the screen the greatest?
Translated by SOTA. The Russian original is the official version and wins wherever the two differ. 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
- Written solution (proof or answer with justification), graded by the criteria in the official solutions file.
- Scoring
- Points awarded by the published criteria (partial credit for stated intermediate results; deductions for gaps).
- Rules
- Written tour; no computer-based submission.
- Format
- Final stage, Tour 1 (theoretical), Moscow, 23 March 2026; grades 9–11; individual written tour.