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Omni-MATH / In the plane we consider rectangles whose sides are parallel to the coordinate…

Problem

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problem

In the plane we consider rectangles whose sides are parallel to the coordinate axes and have positive length. Such a rectangle will be called a [i]box[/i]. Two boxes [i]intersect[/i] if they have a common point in their interior or on their boundary. Find the largest n n for which there exist n n boxes B1 B_1, … \ldots, Bn B_n such that Bi B_i and Bj B_j intersect if and only if $ i\not\equiv j\pm 1\pmod n$. [i]
Plain-text mathematical notation (without MathML)
In the plane we consider rectangles whose sides are parallel to the coordinate axes and have positive length. Such a rectangle will be called a [i]box[/i]. Two boxes [i]intersect[/i] if they have a common point in their interior or on their boundary. Find the largest n for which there exist n boxes B₁, …, B_(n) such that B_(i) and B_(j) intersect if and only if $ i\not\equiv j\pm 1\pmod n$.

[i]
Original LaTeX notation
In the plane we consider rectangles whose sides are parallel to the coordinate axes and have positive length. Such a rectangle will be called a [i]box[/i]. Two boxes [i]intersect[/i] if they have a common point in their interior or on their boundary. Find the largest $ n$ for which there exist $ n$ boxes $ B_1$, $ \ldots$, $ B_n$ such that $ B_i$ and $ B_j$ intersect if and only if $ i\not\equiv j\pm 1\pmod n$.

[i]

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Source and history

task_id
d024229f-232f-522f-a02c-0ff064323c2e
task_key
test--d024229f-232f-522f-a02c-0ff064323c2e
task_revision_id
1
config / split
/ test

Official source

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