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MathNet 2021 — Part 10 Question 27

Math Olympiad Vault · MathNet 2021 — Part 10

Question 27

Is it possible to fill an $n\times n$ table with numbers $1$ and $2$ such that the sum of the numbers in each column is a multiple of $5$ and the sum of the numbers in each row is a multiple of $7$? Solve this:

- **(a)** for $n=9$.
- **(b)** for $n=12$.

(Tomáš Bárta)