Checklist VsOSh AI 2026 School Stage (Sirius platform, region group 1), grades 9–11 · Task 2
Forecasting Task Types
Russian title: Задание 2
Choose between two all-or-nothing forecasting strategies and compute the expected number of correct guesses.
The task
In an online olympiad each participant gets three tasks, each either mathematics or AI. In the new season the task type at position i stays the same as last year with probability s_i and flips otherwise, independently: s₁ = 2/3, s₂ = 1/3, s₃ = 3/4. Petya will predict either that no type changes or that every type flips.
Which prediction maximises the expected number of correctly guessed positions, and what is that expectation?
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.
- Task statement Russian original of Task statement
- Official solution Russian original of Official solution
- Full paper with solutions (all tasks of the tour) Russian original of Full paper with solutions (all tasks of the tour)
Read the task statement in English
Forecasting Task Types
English translation by SOTA – AI Community of the Russian original. Organisers who would like this translation removed can email [email protected].
Task 2 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.
At the qualifying stage of an online olympiad, each participant is given three problems, each of which is either in mathematics or in artificial intelligence. Suppose that in the new season the problem type at position coincides with last year's with probability and switches to the opposite with probability . The choice is made independently for different positions. It is known that . Petya has analysed last year's problem sets and is sure that, even before the round starts, he can predict the problem types at all three positions at once: either none of them will change and they will be the same as last year, or all of them will switch to the opposite (that is, artificial intelligence will come up instead of mathematics, and vice versa).
Petya wants the average number of correctly guessed positions (the mathematical expectation) to be as large as possible. Which prediction is optimal in this case?
- The problem types will not change
- The problem types will switch to the opposite
Find the average number of positions (the mathematical expectation) guessed correctly by Petya if he follows the optimal strategy.
Scoring criterion: 6 points for each correct answer. Total — 12 points
Maximum score for the task — 12
Translated by SOTA. The Russian original is the official version and wins wherever the two differ. Statement and official solution come from one PDF, the analysis of the school-stage tasks for region group I, grades 9–11, linked from the olympiad's Sirius page. 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
- The optimal strategy (one of two options) and the expected number.
- Scoring
- Two answers, 6 points each (12 in total).
- Format
- School stage on the Sirius.Courses platform, region group 1, 23 October 2025; grades 9–11; individual; 150 minutes; maximum 112 points for the paper (tasks 1–6: 12 points each; tasks 7–8: 20 points each).