From 1977 to 2025, four Vietnamese math problems have been featured in official IMO exams.
Four mathematics problems written by Vietnamese authors have been chosen for the official exams of the International Mathematical Olympiad (IMO), the latest being a geometry problem by Tran Quang Hung, a teacher at the High School for Gifted Students under the University of Science, Vietnam National University, Hanoi.
Tran Quang Hung’s problem – IMO 2025
The problem authored by Tran Quang Hung selected as Problem 2 at IMO 2025.
At the 2025 IMO, the only geometry problem in the test - Problem 2 on Day 1 - was proposed by Vietnam and authored by teacher Tran Quang Hung. He currently teaches at the High School for Gifted Students, University of Science, Vietnam National University, Hanoi.
This marks the fourth time a Vietnamese-authored problem has been featured in an official IMO exam, following appearances in 1977 (by Phan Duc Chinh), 1982 (by Van Nhu Cuong), and 1987 (by Nguyen Minh Duc).
Phan Duc Chinh’s problem – IMO 1977
The 1977 IMO problem by Phan Duc Chinh, presented by the Vietnam Institute for Advanced Study in Mathematics.
Problem 2 in the 1977 IMO exam was authored by Phan Duc Chinh:
“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.”
The late Assoc. Prof. Dr. Phan Duc Chinh (1936–2017) was among the first instructors of Class A0 - the predecessor to today’s specialized math class at the High School for Gifted Students, University of Science, Vietnam National University, Hanoi. He trained numerous IMO medalists and served as deputy and head of Vietnam’s IMO delegation. He also authored and translated many classic mathematics textbooks in Vietnam.
Van Nhu Cuong’s problem – IMO 1982
The 1982 IMO problem by the late Assoc. Prof. Van Nhu Cuong.
Problem 6 in the 1982 IMO exam was written by the late Assoc. Prof. Dr. Van Nhu Cuong:
“Let S be a square with side length 100. Let L be a path within S composed of line segments A₀A₁, A₁A₂, ..., Aₙ₋₁Aₙ with A₀ ≠ Aₙ. Suppose that for every point P on the boundary of S there is a point of L within distance 1/2 from P. Prove that there exist two points X and Y on L such that the distance between them is no greater than 1 and the length of the part of L between X and Y is at least 198.”
The problem was noted for being not only challenging but also original. According to Prof. Tran Van Nhung, former Deputy Minister of Education and Training, some countries initially opposed the inclusion of the problem in the exam, but the IMO Chair decided to retain it and praised it as “excellent.”
Interestingly, the original version of the problem featured poetic imagery, describing a village, a river, and a square layout, but these elements were later rewritten in standard mathematical language for the exam.
Prof. Ngo Bao Chau once remarked that this was one of the most beautiful and intriguing problems in IMO history.
The late Assoc. Prof. Dr. Van Nhu Cuong (1937–2017) was a respected educator and the founder of Luong The Vinh High School, Vietnam’s first private high school. He authored numerous geometry textbooks and served as a member of the National Education Council.
Original version of Van Nhu Cuong’s problem:
“Once upon a time, there was a square-shaped village, 100 km per side, with a river winding through it. Any point in the village was no more than 0.5 km from the river. Prove that there exist two points on the river less than 1 km apart as the crow flies, but with a river path distance of no less than 198 km.” (Assuming the river’s width is negligible.)
Nguyen Minh Duc’s problem – IMO 1987
The 1987 IMO problem by Dr. Nguyen Minh Duc.
Problem 4 in the 1987 IMO exam was authored by Dr. Nguyen Minh Duc:
“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.”
Dr. Nguyen Minh Duc is an alumnus of the High School for Gifted Students, University of Science, and won a silver medal at the 1975 IMO. Before retirement, he worked as 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 1974.
Each year, national team leaders submit problem proposals to the host country’s selection committee. Authors need not be part of the delegation but must be nationals of the proposing country. From over 100 annual submissions, the host nation typically shortlists around 30 problems. A final vote among team leaders a few days before the exam determines the six official problems.
Vietnamnet.vn
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