# Falsifying a Hypothesis

*English translation by SOTA – AI Community of the Russian original. Organisers who would like this translation removed can email sota.ai.community@gmail.com.*

*Task 4 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.*

A teacher explains to the children that if they want to test a hypothesis, they must try to refute it. He has thought of a rule that the triple of integers 1, 2, 4 satisfies. It is known that this rule is one of four:

- the numbers are strictly increasing;
- all the numbers are positive;
- any three numbers fit;
- the product of the first and the last numbers equals the square of the second.

Choose two triples of numbers such that the pair of “yes/no” answers makes it possible to determine unambiguously which of the four rules has been thought of:

*[The answer options are not listed in the original file; the table in the solution considers the triples (1, 2, 4), (1, 2, 3), (−3, −3, −3) and (−3, −2, −1).]*

**Scoring criterion:** (Number of correct choices minus number of incorrect ones) × 6, maximum 12 points

**Maximum score for the task — 12**