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OlympiadBench / 2064 / In the plane, 2013 red points and 2014 blue points are marked so that no three…

Problem

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

question

In the plane, 2013 red points and 2014 blue points are marked so that no three of the marked points are collinear. One needs to draw

k

lines not passing through the marked points and dividing the plane into several regions. The goal is to do it in such a way that no region contains points of both colors. Find the minimal value of

k

such that the goal is attainable for every possible configuration of 4027 points.

Plain-text mathematical notation (without MathML)

In the plane, 2013 red points and 2014 blue points are marked so that no three of the marked points are collinear. One needs to draw k lines not passing through the marked points and dividing the plane into several regions. The goal is to do it in such a way that no region contains points of both colors.

Find the minimal value of k such that the goal is attainable for every possible configuration of 4027 points.

Original LaTeX notation

In the plane, 2013 red points and 2014 blue points are marked so that no three of the marked points are collinear. One needs to draw $k$ lines not passing through the marked points and dividing the plane into several regions. The goal is to do it in such a way that no region contains points of both colors.

Find the minimal value of $k$ such that the goal is attainable for every possible configuration of 4027 points.

answer type

Numerical

is multiple answer

false

language

English

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 2064
task_id: fbc3bb67-a0c4-5b25-a071-8f15612cd465
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2064
task_revision_id: 3
config / split: OE_TO_maths_en_COMP / train

Official source

initial import