National excellent student competition: math exam questions and solutions for day two

The national excellent student competition's math exam for day two, held on the morning of 26/12, featured three questions for nearly 680 contestants, including a real-world problem based on the character Mario's game.

This academic year's national excellent student competition took place on 25-26/12, involving over 6,750 students, an increase of 270 participants from the previous academic year.

Students competed in 13 subjects. Literature had the highest number of contestants with 709, followed by English and Geography, each with over 680 participants.

Yesterday, contestants completed their day one exams. Today, in addition to math, students also took written exams in physics, chemistry, and biology; programming exams for informatics; and speaking exams for five foreign languages.

Following mergers, the country now has 42 participating delegations, comprising 34 provinces and cities, along with universities such as Vietnam National University, Hanoi; Vietnam National University, Ho Chi Minh City; Hue University; Hanoi National University of Education; Ho Chi Minh City University of Education; Vinh University; Tan Tao University; and Viet Bac High School for Ethnic Minorities.

According to regulations from the Ministry of Education and Training, 60% of contestants will receive awards. Among these, the number of first, second, and third prizes will not exceed 60% of the total awards, and first prizes will not exceed 5%.

Students who achieve national awards receive certificates and are granted direct admission to universities. Additionally, they receive local policy-based rewards, typically ranging from 10 to 100 million VND.

For the five international Olympiad subjects—math, physics, chemistry, informatics, and biology—the Ministry of Education and Training will invite high-scoring contestants (typically the top 40) for training before the team selection competition.

Below are detailed solutions provided by: Vo Quoc Ba Can, Nguyen Le Phuoc, Nguyen Tien Dung (teachers at Archimedes Academy, Hanoi); Phan Quang Linh (Giang Vo Secondary School); Tran Duc Hieu (Hanoi - Amsterdam High School for the Gifted); Tran Quang Do, Vu Minh Duc, Nguyen Van Quy (CMATH Club); Dao Phuc Long (student at Hanoi University of Science and Technology); and Vuong Khanh Toan (student at University of Science, Vietnam National University, Hanoi).