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OlympiadBench / 1641 / Let n be a positive integer and fix 2n distinct points on a circumference.…

Problem

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

question

Let

n

be a positive integer and fix

2 n

distinct points on a circumference. Split these points into

n

pairs and join the points in each pair by an arrow (i.e., an oriented line segment). The resulting configuration is good if no two arrows cross, and there are no arrows

\overrightarrow{A B}

and

\overrightarrow{C D}

such that

A B C D

is a convex quadrangle oriented clockwise. Determine the number of good configurations.

Plain-text mathematical notation (without MathML)

Let n be a positive integer and fix 2n distinct points on a circumference. Split these points into n pairs and join the points in each pair by an arrow (i.e., an oriented line segment). The resulting configuration is good if no two arrows cross, and there are no arrows (AB)→ and (CD)→ such that ABCD is a convex quadrangle oriented clockwise. Determine the number of good configurations.

Original LaTeX notation

Let $n$ be a positive integer and fix $2 n$ distinct points on a circumference. Split these points into $n$ pairs and join the points in each pair by an arrow (i.e., an oriented line segment). The resulting configuration is good if no two arrows cross, and there are no arrows $\overrightarrow{A B}$ and $\overrightarrow{C D}$ such that $A B C D$ is a convex quadrangle oriented clockwise. Determine the number of good configurations.

answer type

Expression

is multiple answer

false

language

English

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 1641
task_id: f7a41ad3-8a00-54bb-8911-582cdb4c860f
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--1641
task_revision_id: 3
config / split: OE_TO_maths_en_COMP / train

Official source

initial import