Checklist VsOSh AI 2026 Final Stage, Tour 1 (theory) · A task
The Line Rotates Again
Russian title: Прямая снова крутится
Choose integer parameters so that a linear classifier separates three points lying on a quadratic.
The task
A linear classifier on the plane is given by the line x + Ay = 0: a point (x, y) belongs to class 1 if x + Ay > 0 and to class 2 otherwise.
Give an example of integers A, b and c such that, for the trinomial P(x) = x² + bx + c, the point (2, P(2)) belongs to class 1 while the points (1, P(1)) and (3, P(3)) belong to class 2.
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 17 September 2026.
- Task statement Russian original of Task statement
- Official solution Russian original of Official solution
- Full paper (all tasks of the tour) Russian original of Full paper (all tasks of the tour)
- All solutions of the tour with marking criteria Russian original of All solutions of the tour with marking criteria
Read the task statement in English
The Line Rotates Again
English translation by SOTA – AI Community of the Russian original. Organisers who would like this translation removed can email [email protected].
All-Russian School Olympiad in Informatics 2025–2026, Final Stage
“Artificial Intelligence” profile, Tour 1, Moscow, 23 March 2026
Task A
Consider a linear classifier on the plane defined by the line . A point belongs to the first class if . Otherwise, if , the point belongs to the second class.
Give an example of integers , and such that, for the trinomial , the point belongs to the first class, while the points and belong to the second class.
Translated by SOTA. The Russian original is the official version and wins wherever the two differ. 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
- Written solution (proof or answer with justification), graded by the criteria in the official solutions file.
- Scoring
- Points awarded by the published criteria (partial credit for stated intermediate results; deductions for gaps).
- Rules
- Written tour; no computer-based submission.
- Format
- Final stage, Tour 1 (theoretical), Moscow, 23 March 2026; grades 9–11; individual written tour.