Checklist VsOSh AI 2026 School Stage (Sirius platform, region group 3), grades 9–11 · Task 1
Independent Groups in Federated Learning
Russian title: Задание 1
Find the maximum number of connected components of a graph with 10 vertices and 10 edges.
The task
In federated learning, 10 devices exchange data over two-way channels; there are 10 channels in total, at most one per pair of devices. An independent group is a set of devices connected by chains of channels with no channel to other groups.
What is the largest possible number of independent groups?
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 3 files into English on 16 September 2026.
- Task statement Russian original of Task statement
- Official solution Russian original of Official solution
- Full paper with solutions (all tasks of the tour) Russian original of Full paper with solutions (all tasks of the tour)
Read the task statement in English
Independent Groups in Federated Learning
English translation by SOTA – AI Community of the Russian original. Organisers who would like this translation removed can email [email protected].
Task 1 of the school stage of the All-Russian School Olympiad (VsOSh) 2025/26 in artificial intelligence (region group III), grades 9–11. The official answer and solution are in a separate file.
In collaborative learning (it is also called federated learning), many devices learn together: each one computes locally and sends only a small share of the total volume of numerical data. For this exchange, two-way communication channels have been laid between some pairs of devices. The task is performed by 10 devices. Two-way channels have been laid between some pairs of devices, 10 channels in total (there is never more than one channel between the same pair of devices). We call a group of devices an independent group if any device in it can be reached from any other via a chain of channels, and there is not a single channel between different such groups. What is the largest number of independent groups that can be obtained under these conditions?
Scoring criterion: exact match of the answer — 12 points
Maximum score for the task — 12
Translated by SOTA. The Russian original is the official version and wins wherever the two differ. Statement and official solution come from one PDF, the analysis of the school-stage tasks for region group III, grades 9–11, linked from the olympiad's Sirius page. 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
- One number.
- Scoring
- Exact answer; 12 points.
- Format
- School stage on the Sirius.Courses platform, region group 3, 20 October 2025; grades 9–11; individual; 150 minutes; maximum 112 points for the paper (tasks 1–6: 12 points each; tasks 7–8: 20 points each).