# Guess the Coefficients

*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 2 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).*

Petya has thought of two natural numbers $a$ and $b$. Vasya is trying to guess them by asking questions. A question from Vasya consists of him naming two natural numbers $x$ and $y$. In reply to a question, Petya reports two numbers $z < t$, one of which is equal to $ax + by$ (he does not say which one).

Vasya asked two questions: for $x = 4$ and $y = 1$, Petya replied 14 and 15; for $x = 1$ and $y = 4$, Petya replied 9 and 11. Which numbers did Petya think 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).*