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MathNet 2026 — Part 03 Question 90

Math Olympiad Vault · MathNet 2026 — Part 03

Question 90

Will there be 16 different natural numbers and less than 100 such that when placed in the boxes of a board $4 \times 4$ the product of those located in each row is the same and, in turn, coincides with that of those placed in each column and on the two main diagonals? If the answer is yes, indicate which ones they are. If the answer is negative, justify it.