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Checklist VsOSh AI 2026 Regional Stage, Tour 1 (mathematics) · A task

Natural Numbers

Russian title: Натуральные числа

Recover the possible values of an erased first term of a sequence in which each term is the sum of all previous ones.

  • Number theory
  • Russian original · English translation

The task

One hundred natural numbers were written in a row: the second equals 1, and every number from the third onwards equals the sum of all previously written numbers. The first number was then erased, and one of the remaining numbers turned out to equal 123456123456123456.

What could the erased number have been?

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. Only the words changed in the notebooks: markdown, code comments, messages and printed output. The code, file names and paths are the original's, so a translated notebook runs with the original data.

Read the task statement in English 172 words

Natural Numbers

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, Regional Stage, Grades 9–11
“Artificial Intelligence” profile, Tour 1, 17 January 2026
Task A

Points for the task: 50
Answer submission format: entering the answer
Number of attempts: 10
Submission that counts: the last one

Statement

One hundred natural numbers were written in a row, one after another. The second number was equal to 1, and each number, starting from the third, is equal to the sum of all the numbers written before it. Then the first number was erased. It turned out that one of the remaining numbers is equal to 123456123456123456. What could the erased number have been?

Output format

As your answer, output all suitable values in ascending order, separated by spaces.

Scoring

An exact match of the answer: 50 points.

Test results are not available during the tour.

Translated by SOTA. The Russian original is the official version and wins wherever the two differ. The statement is translated from the tour's PDF paper; the official editorial is a single notebook covering all tasks of the tour. 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
All possible values in increasing order, separated by spaces.
Scoring
Answer entry; 50 points for an exact match; 10 attempts, the last one counts; results hidden during the tour.
Rules
  • Python may be used, or the problem may be solved purely mathematically.
Format
Regional stage, Tour 1, 17 January 2026; grades 9–11; individual; 300-minute tour (Moscow procedure); answers entered in Yandex Contest.

Details

Year
2026, Regional venues across Russia (in person)
Round
Regional Stage, Tour 1 (mathematics) · A task
Language
Russian; English translation by SOTA
License
Not stated by the source