# Guess the Coefficients: Official Solution

*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: official answer and solution (the statement is in a separate file). Original: [sol-ai-9-11-sch-msk-25-26.pdf](https://vos.olimpiada.ru/upload/files/Arhive_tasks/2025-26/school/ai/sol-ai-9-11-sch-msk-25-26.pdf).*

**Answer:** $a = 3,\ b = 2$

**Scoring criterion:** exact match of the answer — 12 points

**Maximum score for the task — 12**

**Solution.**

Note that in both questions $x + y = 5$. Hence the correct answers to the two questions (one from each pair) add up to

$$
(ax + by) + (ax' + by') = a(x + x') + b(y + y') = 5(a + b),
$$

that is, their sum is divisible by 5.

Of the pairs $\{14, 15\}$ and $\{9, 11\}$, the only combination whose sum is a multiple of 5 is 14 and 11. Consequently,

$$
4a + b = 14, \qquad a + 4b = 11.
$$

Solving, we obtain $a = 3$, $b = 2$.