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Omni-MATH / Given two integers m,n satisfying 4<m<n. Let A_{1}A_{2}cdots A_{2n plus{} 1} be a regular 2nplus{}1 polygon. Denote by P the set of its vertices. Find the number of convex m poly…

Problem

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problem

Given two integers

m,n

satisfying

4 < m < n.

Let $ A_{1}A_{2}\cdots A_{2n \plus{} 1}$ be a regular $ 2n\plus{}1$ polygon. Denote by

P

the set of its vertices. Find the number of convex

m

polygon whose vertices belongs to

P

and exactly has two acute angles.

Plain-text mathematical notation (without MathML)

Given two integers m,n satisfying 4<m<n. Let $ A_{1}A_{2}\cdots A_{2n \plus{} 1}$ be a regular $ 2n\plus{}1$ polygon. Denote by P the set of its vertices. Find the number of convex m polygon whose vertices belongs to P and exactly has two acute angles.

Original LaTeX notation

Given two integers $ m,n$ satisfying $ 4 < m < n.$ Let $ A_{1}A_{2}\cdots A_{2n \plus{} 1}$ be a regular $ 2n\plus{}1$ polygon. Denote by $ P$ the set of its vertices. Find the number of convex $ m$ polygon whose vertices belongs to $ P$ and exactly has two acute angles.

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task_id: 8d72f883-765a-5aa6-8cc0-32cd997b1fc6
task_key: test--8d72f883-765a-5aa6-8cc0-32cd997b1fc6
task_revision_id: 4
config / split: / test

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