Demo 2023 Math Olympiad HSE University Problem 9 Solution

Bear in mind it is only for Ghana and only for math.

Mathematics
180 MINUTES DURATION OF COMPETITION
10 PROBLEMS OF BASIC AND ADVANCED LEVEL

Description of tasks
Competition in Mathematics is held both in in-person format (offline) and remote format (online). Each participant may choose just one of the formats: writing either on a special venue or remotely. Either way a participant has 180 minutes for writing the test.

A task of HSE INTO 2024 in Mathematics consists of 10 problems divided into three blocks according to the problems’ difficulty:

Problems of the first block (from 1st to 6th) are closer to examination tasks, they check knowledge and skills of participants in high school mathematics. These problems suppose just providing an answer without explanations. The problems are graded 7 points for correct answers and 0 points for incorrect one.
Problems of the second block (7th and 8th) are out of scope of standard high school mathematics and use more technical approaches of advanced classes of mathematics. These problems are marked in a range from 0 to 13 points. Both answer and sketch of a proof (proof scheme) are needed here.
Problems of the third block (9th and 10th) are close to national high school competitions in mathematics and to the International mathematical Olympiad in their style, program, and difficulty. Full solution with all intermediate steps should be given for these problems. The problems are marked in a range from 0 to 16 points.
Thus, problems number 7 to 10 suppose writing a partial or full solution. Online participants enter their solutions to a special web form on the competition platform using a standard keyboard.

Competition problems demand from participants not just knowledge but also creativity, reasoning skills, analysis of the computational results, skills of making conjectures and of verification of the conjectures.

REFERENCE MATERIALS FOR TEACHERS

Examples of Undergraduate Programs which accept winners
Economics (Moscow)
Economics and Statistics (Moscow)
Economics and Data Science (Moscow)
Applied Mathematics (Moscow)
Applied Mathematics and Information Science (Moscow)
Business Administration (Moscow)
Business Informatics (Moscow)
Chemistry (Moscow)
Cyber Security (Moscow)
Fundamental and Computational Linguistics (Moscow)
Geography of Global Changes and Geoinformation Technology (Moscow)
Information and Communication Technologies and Systems (Moscow)
Information Security (Moscow)
Information Science and Computation Technology (Moscow)
Marketing and Market Analytics (Moscow)
Physics (Moscow)
Physics (Saint Petersburg)
Psychology (Moscow)
Public Administration (Moscow)
Sociology (Moscow)
Software Engineering (Moscow)
Supply Chain Management and Business Analytics (Moscow)
Urban Planning (Moscow)
World Economy (Moscow)