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Checklist VsOSh AI 2026 School Stage (Moscow), grades 9–11 · Task 4

Minimise the Loss

Russian title: Задание 4

Find the minimiser and the minimum of a two-parameter polynomial loss function.

  • Optimisation (completing the square)
  • Russian original · English translation

The task

Vasya found that the loss of his model with real parameters x and y is L(x, y) = x⁴ + y² + 2x²y + 4y + 6x² − 4x + 14.

Find the parameters (x*, y*) that minimise the loss and the value L(x*, y*).

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 182 words

Minimise the Loss

English translation by SOTA – AI Community of the Russian original. Organisers who would like this translation removed can email [email protected].

Task 4 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.

Vasya was testing a model with real parameters xx and yy. He found out that the loss function is given by the formula

L(x,y)=x4+y2+2x2y+4y+6x24x+14.\mathcal{L}(x, y) = x^4 + y^2 + 2x^2y + 4y + 6x^2 - 4x + 14.

Help Vasya determine the values of the parameters (x,y)(x^*, y^*) for which the value of the loss function is smallest. In your answer, give xx^*, yy^* and the value L(x,y)\mathcal{L}(x^*, y^*).

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
x*, y* and L(x*, y*).
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 4
Language
Russian; English translation by SOTA
License
Not stated by the source