Checklist VsOSh AI 2026 School Stage (Moscow), grades 9–11 · Task 5
Two Positive Examples
Russian title: Задание 5
Find the dataset sizes for which drawing both positives in a random group of four is twice as likely as drawing none.
The task
A training set has N examples, exactly two of which are positive. A group of 4 examples is chosen at random, and the probability that the group contains both positives is twice the probability that it contains none.
Find all possible values of N.
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 16 September 2026.
- Task statement Russian original of Task statement
- Official solution Russian original of Official solution
- Full paper (all tasks of the stage) Russian original of Full paper (all tasks of the stage)
- All solutions of the stage Russian original of All solutions of the stage
Read the task statement in English
Two Positive Examples
English translation by SOTA – AI Community of the Russian original. Organisers who would like this translation removed can email [email protected].
Task 5 of the school stage (Moscow) of the All-Russian School Olympiad (VsOSh) 2025/26 in artificial intelligence, grades 9–11. Original: tasks-ai-9-11-sch-msk-25-26.pdf.
There is a set of training examples: examples in total, of which exactly two are positive and the rest are negative. A group of 4 examples is chosen at random. It is known that the probability that the group contains both positive examples is 2 times the probability that it contains no positive example at all. Find all possible values of .
Translator's note: the statement paper gives only the total for the olympiad (112 points); the official solutions give this task a maximum of 12 points (exact match of the answer).
Translated by SOTA. The Russian original is the official version and wins wherever the two differ. Translated from the statement and solution PDFs of the Moscow school stage (grades 9–11) on vos.olimpiada.ru. The statement paper gives no per-task points; the 12 points come from the official solutions. 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
- All possible N.
- Scoring
- Exact answer (points per task are not stated in the statement file).
- Format
- School stage (Moscow), started 24 October 2025, grades 9–11; individual; online testing system; maximum 112 points for the paper.