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OlympiadBench / 2174 / A plane has a special point O called the origin. Let P be a set of 2021…

Problem

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

question

A plane has a special point

O

called the origin. Let

P

be a set of 2021 points in the plane, such that (i) no three points in

P

lie on a line and (ii) no two points in

P

lie on a line through the origin. A triangle with vertices in

P

f a t

, if

O

is strictly inside the triangle. Find the maximum number of fat triangles.

Plain-text mathematical notation (without MathML)

A plane has a special point O called the origin. Let P be a set of 2021 points in the plane, such that

(i) no three points in P lie on a line and

(ii) no two points in P lie on a line through the origin.

A triangle with vertices in P is fat, if O is strictly inside the triangle. Find the maximum number of fat triangles.

Original LaTeX notation

A plane has a special point $O$ called the origin. Let $P$ be a set of 2021 points in the plane, such that

(i) no three points in $P$ lie on a line and

(ii) no two points in $P$ lie on a line through the origin.

A triangle with vertices in $P$ is $f a t$, if $O$ is strictly inside the triangle. Find the maximum number of fat triangles.

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: 2174
task_id: d53c9dd8-25a7-52f2-b3d8-49f752c25633
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2174
task_revision_id: 3
config / split: OE_TO_maths_en_COMP / train

Official source

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