# Two Positive Examples

*English translation by SOTA – AI Community of the Russian original. Organisers who would like this translation removed can email sota.ai.community@gmail.com.*

*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](https://vos.olimpiada.ru/upload/files/Arhive_tasks/2025-26/school/ai/tasks-ai-9-11-sch-msk-25-26.pdf).*

There is a set of training examples: $N$ 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 $N$.

*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).*