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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,…

Problem

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problem

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.

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: 2
config / split: / test

Official source

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