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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.

  • Number theory (systems of equations)
  • Russian original · English translation

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.

Read the task statement in English 201 words

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 aa and bb. Vasya is trying to guess them by asking questions. A question from Vasya consists of him naming two natural numbers xx and yy. In reply to a question, Petya reports two numbers z<tz < t, one of which is equal to ax+byax + by (he does not say which one).

Vasya asked two questions: for x=4x = 4 and y=1y = 1, Petya replied 14 and 15; for x=1x = 1 and y=4y = 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).

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.

Details

Year
2026, Moscow, Russia (online testing system)
Round
School Stage (Moscow), grades 9–11 · Task 2
Language
Russian; English translation by SOTA
License
Not stated by the source