Checklist VsOSh AI 2026 School Stage (Sirius platform, region group 4), grades 9–11 · Task 3
Homework or Answer Key
Russian title: Задание 3
Optimise the number of honestly solved homeworks in a model where copying boosts homework marks but not knowledge.
The task
A student has 10 homeworks and one test; knowledge starts at K₁ = 0 and grows by 1 for each homework solved honestly (copying from an answer key does not increase it). An honest homework t scores H_t = 1.5 + 0.3·K_t, a copied one scores 4.5; the test scores E = min{1 + 0.5·K₁₁, 5}; the final mark is S = 0.4·(H₁ + … + H₁₀)/10 + 0.6·E. The statement motivates this by analogy with models that memorise leaked answers.
Find the maximum of S (to three decimal places) and the optimal number of honestly solved homeworks.
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
Homework or Answer Key
English translation by SOTA – AI Community of the Russian original. Organisers who would like this translation removed can email [email protected].
Task 3 of the school stage of the All-Russian School Olympiad (VsOSh) 2025/26 in artificial intelligence (region group IV), grades 9–11. The official answer and solution are in a separate file.
When programs are taught from examples (this is called machine learning), a certain mistake happens: the correct answers accidentally end up in the training examples. The program then does not learn to reason but simply memorises the answers, and fails on new problems. Schoolchildren are in a similar situation: one can honestly work through a topic, or one can copy from “ready-made homework” answer books (GDZ). By copying, it is easy to get high marks, but there is little knowledge, and this will show in the test.
A pupil has 10 homework assignments and one test. For each homework assignment, he chooses either to solve it on his own (H) or to copy it from the GDZ (G).
Let be the level of knowledge before the -th homework assignment (=1, ..., 10). If the pupil solves assignment himself, his level of knowledge increases by one; otherwise the level of knowledge does not increase; .
The mark for the -th homework assignment is calculated as follows: if it was solved honestly, then ; if the homework was copied, then .
The mark for the test depends only on the knowledge after the last homework assignment, :
The final average mark: 40% for the homework, 60% for the test:
Find the maximum value of . Round the answer to thousandths.
Find the optimal number of honestly completed homework assignments at which is maximal.
Scoring criterion: 6 points for each correct answer. Total — 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 IV, grades 9–11, linked from the olympiad's Sirius page. The original writes the maximum with a decimal comma (4,176); the translation writes 4.176. 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
- Two numbers.
- Scoring
- Two answers, 6 points each (12 in total).
- Format
- School stage on the Sirius.Courses platform, region group 4, 21 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).