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Omni-MATH / Given positive integers n and k, n>k²>4. In a n×n grid, a k[i]-group[/i] is a set of k unit squares lying in different rows and different columns. Determine the maximal possible N,…

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problem

Given positive integers nn and kk, n>k2>4.n > k^2 >4. In a n×nn \times n grid, a kk[i]-group[/i] is a set of kk unit squares lying in different rows and different columns. Determine the maximal possible NN, such that one can choose NN unit squares in the grid and color them, with the following condition holds: in any kk[i]-group[/i] from the colored NN unit squares, there are two squares with the same color, and there are also two squares with different colors.
Plain-text mathematical notation (without MathML)
Given positive integers n and k, n>k²>4. In a n×n grid, a k[i]-group[/i] is a set of k unit squares lying in different rows and different columns.
Determine the maximal possible N, such that one can choose N unit squares in the grid and color them, with the following condition holds: in any k[i]-group[/i] from the colored N unit squares, there are two squares with the same color, and there are also two squares with different colors.
Original LaTeX notation
Given positive integers $n$ and $k$, $n > k^2 >4.$ In a $n \times n$ grid, a $k$[i]-group[/i] is a set of $k$ unit squares lying in different rows and different columns.
Determine the maximal possible $N$, such that one can choose $N$ unit squares in the grid and color them, with the following condition holds: in any $k$[i]-group[/i] from the colored $N$ unit squares, there are two squares with the same color, and there are also two squares with different colors.

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Source and history

task_id
2e9656c9-20cb-5391-9c26-c26f8bef5d79
task_key
test--2e9656c9-20cb-5391-9c26-c26f8bef5d79
task_revision_id
5
config / split
/ test

Official source

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