Math problem by author Tran Quang Hung - IMO 2025
Recently, at the 2025 International Mathematical Olympiad, the only geometry problem in the exam was problem number 2, proposed by Vietnam and authored by Mr. Tran Quang Hung, a teacher at the High School for the Gifted in Natural Sciences , University of Natural Sciences , Vietnam National University, Hanoi.
The problem chosen as question number 2 in the 2025 International Math Olympiad exam day 1 by author Tran Quang Hung is as follows:
Pandemic:
This is the fourth time Vietnam has had a problem selected for the official IMO exam, after 1977 (author: Phan Duc Chinh), 1982 (author: Van Nhu Cuong) and 1987 (author: Nguyen Minh Duc).
Math problem by author Phan Duc Chinh - IMO question in 1977
The problem chosen as question number 2 in the 1977 International Mathematical Olympiad exam by author Phan Duc Chinh is as follows:
“In a finite sequence of real numbers, the sum of any seven successive terms is negative, and the sum of any eleven successive terms is positive. Determine the maximum number of terms in the sequence”.
Pandemic:
In a finite sequence of real numbers, the sum of any 7 consecutive terms is always negative and the sum of any 11 consecutive terms is positive. Determine the maximum number of terms in the sequence.
The problem of Associate Professor Phan Duc Chinh in the 1977 IMO exam, presented again by the Institute for Advanced Study in Mathematics.
The late Associate Professor, Dr. Phan Duc Chinh (1936-2017) was one of the first teachers of the specialized Math class A0, University of General Sciences (now the specialized Math class, High School for the Gifted in Natural Sciences, University of Natural Sciences, Vietnam National University, Hanoi ).
He has trained many excellent students who won medals in International Mathematics; he was the deputy head and head of the Vietnamese delegation to attend IMO. He also wrote and translated many classic Mathematics textbooks in Vietnam.
Math problem by author Van Nhu Cuong - IMO question in 1982
The problem chosen as question number 6 in the 1982 International Mathematical Olympiad exam by author Van Nhu Cuong is as follows:
“Let S be a square with side length 100. Let L be a path within S which is composed of line segments A0A1, A1A2, A2A3..., A(n-1)An with A0 ≠ An. Suppose that for every point P on the boundary of S there is a point of L at a distance from P no greater than 1/2. Prove that there are two points X and Y of L such that the distance between X and Y is not greater than 1 and the length of the part of L which lies between X and Y is not smaller than 198”.
Pandemic:
Let S be a square with side length 100. L is a non-self-intersecting zigzag line formed by line segments A0A1, A1A2..., A(n-1)An with A0 ≠ An. Suppose that for every point P on the perimeter of S there exists a point in L that is no more than 1/2 away from P.
Prove that: There exist 2 points X and Y belonging to L such that the distance between X and Y does not exceed 1, and the length of the broken line L between X and Y is not less than 198.
Math problem of the late Associate Professor Van Nhu Cuong in the 1982 IMO exam.
The problem of the late Associate Professor Van Nhu Cuong in 1982 was considered not only very difficult but also unique. According to Professor Tran Van Nhung, former Deputy Minister of Education and Training, many countries wanted to remove this problem from the exam, but the President of IMO that year decided to keep it and praised it as "very good".
However, the problems in the official exam have been modified. The poetic data with "village" and "river" in the original exam have also been transformed into more mathematical language.
Professor Ngo Bao Chau also rated Mr. Van Nhu Cuong's problem as one of the best and most interesting problems in IMO history.
The late Associate Professor, Dr. Van Nhu Cuong (1937-2017) was a teacher, compiler of high school textbooks and university geometry curriculum, member of the National Education Council of Vietnam. He was also the founder of the first private school in Vietnam, Luong The Vinh High School (Hanoi).
Math problem by author Nguyen Minh Duc - IMO question in 1987
The problem chosen as question number 4 in the 1987 International Mathematical Olympiad exam by author Nguyen Minh Duc is as follows:
“Prove that there is no function f from the set of non-negative integers into itself such that f(f(n)) = n + 1987 for every n”.
Translation: Prove that there does not exist a function f defined on the set of non-negative integers, satisfying the condition f(f(n)) = n + 1987 for all n.
Dr. Nguyen Minh Duc's problem in the 1987 IMO exam.
Dr. Nguyen Minh Duc is a former student of the High School for the Gifted in Natural Sciences, who won a Silver Medal at the IMO in 1975. Before retiring, Dr. Duc was a researcher at the Institute of Information Technology under the Vietnam Academy of Science and Technology.
The International Mathematical Olympiad (IMO) has been held annually since 1959. Vietnam began participating in this competition in 1974.
According to the procedure, before the exam, the head of each country's delegation will collect proposed problems and send them to the selection committee of the country hosting the exam. The authors of the problems from each country do not necessarily have to be members of the delegation, but only need to be from that country.
Typically, more than 100 entries are submitted each year. The host country will shortlist about 30 entries. A few days before the exam, the heads of delegations from each country will vote to select the six official entries for that year's exam.
Source: https://vtcnews.vn/4-bailouts-of-vietnamese-authors-are-chosen-for-the-international-olympic-exams-ar955422.html
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