Checklist VsOSh AI 2026 School Stage (Sirius platform, region group 1), grades 9–11 · Task 1
Shuffled Safe Codes
Russian title: Задание 1
Find the probability that a random permutation of four one-hot safe codes leaves at least one code in place.
The task
Four safes numbered 1–4 have electronic locks whose correct 4-digit binary code has a 1 in the position of the safe number and 0 elsewhere (safe 3: 0010). After the safes are closed, a server permutes the four codes so that all 24 permutations are equally likely.
With what probability does at least one safe receive its correct code again?
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
Shuffled Safe Codes
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 I), grades 9–11. The official answer and solution are in a separate file.
In the Unsafe Vault there are four safes numbered 1, 2, 3, 4. The safes are not labelled, but the staff know which is which. The safes are fitted with electronic combination locks; a code consists of 4 digits, each of which is either 0 or 1. In the correct code, the position whose number equals the safe's number holds a one, and all the other positions hold zeros. For example, the code for safe number 3 is 0010. After the safes are closed, the electronic locks are connected to a server, which swaps the four existing codes around so that all 24 possible permutations are equally likely.
What is the probability that at least one safe gets its correct code again?
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 I, 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
- A probability (fraction).
- Scoring
- Exact answer; 12 points.
- Format
- School stage on the Sirius.Courses platform, region group 1, 23 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).