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OlympiadBench / 2126 / In the coordinate plane consider the set S of all points with integer…

Problem

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

question

In the coordinate plane consider the set

S

of all points with integer coordinates. For a positive integer

k

, two distinct points

A, B \in S

will be called

k

-friends if there is a point

C \in S

such that the area of the triangle

A B C

is equal to

k

. A set

T \subset S

will be called a

k

-clique if every two points in

T

are

k

-friends. Find the least positive integer

k

for which there exists a

k

-clique with more than 200 elements.

Plain-text mathematical notation (without MathML)

In the coordinate plane consider the set S of all points with integer coordinates. For a positive integer k, two distinct points A,B∈S will be called k-friends if there is a point C∈S such that the area of the triangle ABC is equal to k. A set T⊂S will be called a k-clique if every two points in T are k-friends. Find the least positive integer k for which there exists a k-clique with more than 200 elements.

Original LaTeX notation

In the coordinate plane consider the set $S$ of all points with integer coordinates. For a positive integer $k$, two distinct points $A, B \in S$ will be called $k$-friends if there is a point $C \in S$ such that the area of the triangle $A B C$ is equal to $k$. A set $T \subset S$ will be called a $k$-clique if every two points in $T$ are $k$-friends. Find the least positive integer $k$ for which there exists a $k$-clique with more than 200 elements.

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: 2126
task_id: f40ce69e-6f5b-5940-b7ba-f66bc0d292fc
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2126
task_revision_id: 3
config / split: OE_TO_maths_en_COMP / train

Official source

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