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OlympiadBench / 2124 / In the plane we consider rectangles whose sides are parallel to the coordinate…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

answer type

Numerical

is multiple answer

false

language

English

question

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 box. Two boxes intersect 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 $i \not \equiv j \pm 1(\bmod n)$ .

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 box. Two boxes intersect 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 $i \not \equiv j \pm 1(\bmod n)$.

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 box. Two boxes intersect 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 $i \not \equiv j \pm 1(\bmod n)$.

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 2124
task_id: 0145c384-f2d4-5ddb-b392-c22c01ba5c9a
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2124
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

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