Checklist VsOSh AI 2026 School Stage (Moscow), grades 9–11 · Task 2
Guess the Coefficients
Russian title: Задание 2
Recover two hidden natural numbers from two ambiguous answers about linear combinations.
The task
Petya chose natural numbers a and b. For a query (x, y), he reports two numbers z < t, one of which equals ax + by (without saying which). For (x, y) = (4, 1) he answered 14 and 15; for (x, y) = (1, 4) he answered 9 and 11.
Which numbers did Petya choose?
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
Guess the Coefficients
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 (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.
Petya has thought of two natural numbers and . Vasya is trying to guess them by asking questions. A question from Vasya consists of him naming two natural numbers and . In reply to a question, Petya reports two numbers , one of which is equal to (he does not say which one).
Vasya asked two questions: for and , Petya replied 14 and 15; for and , 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).
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
- The numbers a and b.
- 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.