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MathNet 2024-part-03 — 168 problems (EN–VI) Question 95

Math Olympiad Vault · MathNet 2024-part-03 — 168 problems (EN–VI)

Question 95

The numbers $1, 2, \dots, 25$ are written in the cells of a $5 \times 5$ grid as shown below.
Question illustration
Is it possible to make all the numbers in the grid equal by performing a series of operations, where each operation consists of selecting either a row or a column and increasing all the numbers in that row or column by 1?